Basil GRAMMATICOS: a career

Born in Piraeus, Greece on 13/02/1946
Nationalities: Hellenic and French

Diplomas

Diploma of Physical Sciences, University of d'Athens, 1969
DEA de Physique Theorique, University of Paris XI, Orsay, 1972
Doctorat de 3e cycle, University of Paris XI, Orsay, 1974
Doctorat d'Etat es Sciences, University of Paris XI, Orsay, 1977

Positions occupied

Thesis temporary collaborator at CEA, Saclay, 1972-77
Attache de Recherche at CNRS 1977-1981. (CRN of Strasbourg 1977-80)
Transferred to CNET, Issy les Moulineaux, 1980-86
Charge de Recherche at CNRS 1981-1991
Directeur de Recherche at CNRS 1991-
From 1986 to 2006 at GMPIB (ex LPN), University of Paris VII
Since 2006 at IMNC, University of Paris VII-XI-CNRS (UMR 8165), Bat 104, 91406 Orsay
Tel-Fax 33-1-69157201 (e-mail: grammati at paris7 dot jussieu dot .fr)

My main collaborator since more than 30 years: Alfred Ramani

My Scientific activities: a succinct summary

In the remote past (the 70s): Nuclear Physics

-Discovery of triaxial nuclei
-Dynamical effects on spectra and densities
-Estimating the nuclear compressibility
-Splitting and coupling of giant resonances
-Microscopic study of heavy ion fusion

In the less remote past (the 80s): Continuous Dynamical Systems

-Singularity analysis (Painleve method)
-Discovery of new integrable systems
-Quantum integrability
-Rigorous approach to nonintegrability
-Classical and quantum chaos

In the recent past and present(the 90s and 00s): Integrability of Discrete Systems

-Integrability detection: singularity confinement
-Discovery of discrete Painleve equations
-Integrable numerical algorithms
-Ultra-discrete equations
-Geometrical description of discrete Painleve equations

Present and future (the 00s (and 10s)): Modelling of Biological Systems

-Epidemics dynamics
-Description of structures in bacteria colonies
-Gene dynamics
-Migration of tumour cells
-Nonlinear diffusion approach to cell migration

My (long) list of publications

73

1. A semi-classical model for asymmetric fission, B. Grammaticos, Phys. Lett B44, 343 (1973)

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2. Energy surfaces, collective potentials and collective inertia parameters, B. Giraud, B. Grammaticos, Nucl. Phys. A233, 373 (1974)
3. Theorie microscopique du mouvement collectif, B. Giraud, B. Grammaticos, Jour. de Phys. C5, 12 (1974)
4. A solvable model for the monopole vibration, J.P. Blaizot, B. Grammaticos, Phys. Lett B53 231, (1974)
5. Theorie Hartree-Fock des deformations triaxiales statiques et dynamiques, B. Grammaticos, These 3emecycle, Orsay, 1974
6. Collective potentials and inertia parameters, B. Giraud, B. Grammaticos, Nucl. Phys. A255, 141 (1975)
7. Calculation of the static and dynamic triaxial shapes of 24Mg, B. Grammaticos, Nucl. Phys. A252, 90 (1975)

75

8. Microscopic calculation of collective vibrations within the Hartree-Fock approximation, J.P. Blaizot, B. Grammaticos Conf. on H-F and SCF theories, Trieste, 1975, 269
9. A generalized Skyrme interaction with low incompressibility, J.P. Blaizot, B. Grammaticos, K.F. Liu, Conf. on H-F and SCF th;, Trieste, 1975,259
10. Triaxial HartreeFock calculations using Skyrme interaction, B. Grammaticos, Conf. on H-F and SCF theories, Trieste, 1975, 371
11. Non axial vibrations in the adiabatic approximation, B. Grammaticos, Phys. Lett. B57, 306 (1975)
12. Systematics of the proton stripping reaction on 69,71 Ga ,75 As ,79,81 Br isotopes and nuclear structure of the Ge, Se isotopes B. Grammaticos, R. Tamisier et al. Phys. Rev. C12, 1745 ( 1975)
13. Compressibilite et deformabilite des noyaux, J. P. Blaizot, B. Grammaticos, G. Ripka, Jour. de Phys. C5, 21 (1975)
14. A study of monopole and quadrupole vibrations in light deformed nuclei, E. Caurier, B. Grammaticos, XIV Meeting, Bormio, 1976
15. Nuclear compressibility and monopole resonances, J.P. Blaizot, D. Gogny, B. Grammaticos, Nucl Phys. A 265, 315 ( 1976)

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16. On the interpretation of negative collective masses, B. Grammaticos, B. Giraud, Ann. Phys. 101, 670 (1976)
17. Collision of spherical nuclei in 2-D TDHF approach, P. Bonche, A Jaffrin, B. Grammaticos, Congres de la SFP, Caen, 1976
18. Collision of deformed nuclei in 2-D TDHF approach,P. Bonche, A Jaffrin, B. Grammaticos, Congres de la SFP, Caen, 1976
19. Projected spectra of light nuclei with Skyrme interactions, E. Caurier, B. Grammaticos, Nucl. Phys. A 279,333 ( 1976)

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20. Etude microscopique de la triaxialite des noyaux de transition, M. Girod, B. Grammaticos, Congres de la SFP, Poitiers, 1977
21. Static Hartree-Fock- Bogoliubov calculations for triaxial nuclei, M. Girod, B. Grammaticos, In. Cnf. on Nuc. Phys., Tokyo 1977, 71
22. TDHF calculations of 40Ca-40Ca total fusion cross section, P. Bonche, B. Grammaticos, Int. Conf. on Nuc. Phys., Tokyo 1977, 690
23. Splitting of the giant quadrupole resonance in light deformed nuclei, Y. Abgrall, B. Morand, E. Caurier, B. Grammaticos Int. Conf. on Nuc. Physics, Tokyo 1977, 199
24. Splitting of the giant quadrupole resonance in light deformed nuclei, Y. Abgrall, B. Morand, E. Caurier, B. Grammaticos Phys. Rev. Lett. 39, 922 (1977)
25. Developpements recents en physique des ions lourds, P. Bonche, B. Grammaticos, H. Orland, R. Schaeffer, G. Vichniac Note CEA N. 2006 (1977)
26. A Thomas-Fermi study of nuclei at high angular momenta, B. Grammaticos, Phys. Rev. C17, 1244 (1978)
27. The role of the surface in the compression mode of nuclei, J. P. Blaizot, B. Grammaticos, Preprint CEA, DPhT 77/100
28. Application de la theorie du champ self-consistant en Physique Nucleaire, B. Grammaticos, These d'Etat es Sciences, Orsay, 1977
29. Three-dimensional TDHF calculations of 16O-16O and 40Ca-40Ca fusion cross sections, P. Bonche, B. Grammaticos, S. Koonin Phys. Rev. C17, 1700 (1978)
30. The quest for triaxial nuclei : some Hartree-Bogoliubov predictions, M. Girod, B. Grammaticos, Phys. Rev. Lett. 40, 361 (1978)

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31. Cranking calculations with self-consistent symmetries in a triaxial basis, B. Grammaticos, K. F. Liu, Nuov. Cim. A50, 349 (1979)
32. The zero-point energy correction and its effect on nuclear dynamics, M. Girod, B. Grammaticos, Nucl. Phys. A330, 40 (1979)
33. Semi-classical approximations for nuclear Hamiltonians I : spin-independent potentials, B. Grammaticos, A. Voros Ann. Phys. 123, 359 (1979)
34. Calculations of nuclear deformations and collective spectra starting from a density-dependent finite-range nuclear force M. Girod, B. Grammaticos, K. Kumar, P. Aguer, Phys. Rev. Lett. 41, 1765 (1978)
35. Hartree-Fock calculations of crystalline structure of nuclear matter with hard-core potentials, B. Grammaticos, D. Vautherin Phys. Rev. C20, 859 (1979)
36. Fusion cross sections for s-d shell nuclei, S. Koonin, B. Flanders, P. Bonche, B. Grammaticos, H.Flocard, S. Krieger, M. Weiss Bull. APS 23, 955 (1978)

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37. Le dilemme du 12C : spherique ou deforme, E. Caurier, B. Grammaticos, V session d'etudes de Phys. Nucl., Aussois, 1979
38. Shape transition and quadrupole softness in the Ge isotopes, B. Grammaticos, M. Girod, Conf. on med.-heav. nuclei, Rhodes, 1979
39. The fate of the spectators in relativistic heavy-ion collisions, B. Grammaticos, A. Lumbroso, Preprint CEA, DPhT, 79/36
40. Fragmentation des resonances geantes isoscalaires dans les noyaux deformes Y. Abgrall, B. Morand, E. Caurier, B. Grammaticos,V session d'etudes de Phys. Nucl., Aussois, 1979
41. The treatment of residual nuclei in high-energy heavy-ion collisions : a TDHF approach, A. Lumbroso, B. Grammaticos, TDHF workshop, Saclay, 1979
42. TDHF theory and Rayleigh-Ritz principle, B. Giraud, B. Grammaticos, M. Rosina, Phys. Rev. C21, 391 ( 1980)
43. TDHF calculations of fusion cros sections for 16O-40Ca and 28Si-28Si, P. Bonche, B. Grammaticos, K.T.R. Davies, S. Koonin, B. Flanders, H. Flocard, S. Krieger, M. Weiss, Phys. Rev. C20, 641 (1979)
44. The spin components of Skyrme interaction and spectra of light de formed nuclei, E. Caurier, B. Grammaticos, Phys. Lett. 92B, 236 (1980)
45. A solvable model for the study of saturation in finite nuclei, B. Grammaticos, Ann. Phys. 126, 450 (1980)

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46. Semi-classical approximations for nuclear Hamiltonians II : spin-dependent potentials, B. Grammaticos, A. Voros, Ann. Phys. 129, 153 (1980)
47. The breathing mode and the nuclear surface, J.P. Blaizot, B. Grammaticos, Nucl. Phys. A355, 115 (1981)
48. On the fragmentation of the giant isoscalar resonances in deformed nuclei, Y. Abgrall, B. Morand, E. Caurier, B. Grammaticos Nucl. Phys. A346, 431 (1980)
49. A semi-classical model for heavy-ion potentials at high spin, B. Grammaticos, T. Sami, Int. Conf. on High angular momenta, Strasbourg, 1980
50. Review of results obtained for heavy-ion collisions in the TDHF approach, B. Grammaticos, Int. Winter Meeting, Bormio, 1980
51. Triaxial deformation effects in the 2+ transition charge density of 58Ni, M. Girod, B. Frois, B. Grammaticos, Conf on Nucl. Phys., Berkeley, 1980
52. Neutron cross-section calculations for the even Sm isotopes using deformation dep. wave functions M. Girod, C. Lagrange, K. Kumar, B. Grammaticos, Int. Conf on Nucl. Physics, Berkeley, 1980
53. The time-dependent cluster model, E. Caurier, B. Grammaticos, T. Sami, Int. Conf on Nucl. Physics, Berkeley, 1980
54. On the fragmentation of the isoscalar strengths in deformed nuclei, Y. Abgrall, B. Morand, E. Caurier, B. Grammaticos Int. Conf on Nucl. Physics, Berkeley, 1980
55. Giant resonances in the fused system induced by 40Ca-40Ca reactions, P. Bonche, B. Grammaticos, Phys. Lett. 95B,198 (1980)
56. Triaxial deformation effects in the 2+ transition, charge density of 58Ni, M. Girod, B. Frois, B. Grammaticos et al., Colloque PEPS, Saclay, 1980

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57. A mean-field approach for the interpretation of electron scattering experiments: results and perspectives J. Decharge, M. Girod, D. Gogny, B. Grammaticos, Nucl. Phys. A 358, 203c (1981)
58. A semi-classical study of rapidly rotating nuclei, B. Grammaticos, T. Sami, Jour. Phys. G7,1063 (1981)
59. A mean-field approach to the description of nuclear structure : interpretations and predictions B. Grammaticos, Int. Conf. on Nucl. Phys., Bologna, 1980
60. Interpretation microscopique de la densite de transitionn du 58Ni et du 152Sm M. Girod, B. Grammaticos, VI Ses. d'etudes de Phys. Nucl., La Toussuire,1981
61. Leptodermous expansions in nuclei, B. Grammaticos, Workshop on semi-classical approx., Grenoble,1981
62. Dynamical effects in the 2+ transition density of 58Ni, M. Girod, B. Frois, B. Grammaticos, Int. Conf. on Nucl. Phys., Versailles, 1981
63. A study of the leptodermous expansion of the binding energy in finite nuclei, B. Grammaticos, Ann. Phys. 139, 1 (1982)
64. The time-dependent cluster model, B. Grammaticos, E. Caurier, T. Sami, Phys. Lett. 109 B, 150 (1982)
65. A solvable model for the study of the leptodermous expansions in finite nuclei, B. Grammaticos, Zeit. Phys. A 305, 257 (1982)
66. Simulating compressed-air diving : a physicist approach, B. Grammaticos, M. Girod, Preprint CEA-DAM,1982
67. RHI and TDHF : the evolution of the target, B. Grammaticos, A. Lumbroso, Workshop on RHI, Grandlibakken, 1982
68. Sur l'integrabilite du systeme Henon-Heiles, B. Grammaticos, B. Dorizzi, R. Padjen, C.R. Acad. Sci. Paris 294 , 541 (1982)

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69. Painleve property and integrals of motion for the Henon-Heiles system, B. Grammaticos, B. Dorizzi, R. Padjen, Phys. Lett. 89A, 111 (1982)
70. High frequency part of giant resonances, B. Grammaticos, J. Decharge, D. Gogny, L. Sips, Phys. Rev. Lett. 49, 982 (1982)
71. Triaxial Hartree-Fock-Bogoliubov calculations with D1 effective interaction, M. Girod, B. Grammaticos, Phys. Rev. C 27, 2317 (1983)
72. Painleve conjecture revisited, A. Ramani, B. Dorizzi, B. Grammaticos, Phys. Rev. Lett. 49, 1539 (1982)
73. Nouvelles integrales de mouvement pour le systeme de Toda, B. Dorizzi, B. Grammaticos, V. Papageorgiou, R. Padjen, C.R. Acad. Sci. Paris 295 , 321 (1982)
74. On the high frequency part of giant resonances, J. Decharge, D. Gogny, B. Grammaticos, L. Sips, Int. Conf. on Nucl. Phys., Amsterdam, 1982
75. Triaxial structures in nuclei, B. Grammaticos, M. Girod, Int. Conf. on Nucl. Phys., Amsterdam, 1982
76. A new class of integrable systems, B. Dorizzi, B. Grammaticos, A. Ramani, J. Math. Phys., 24, 2282 (1983)
77. Integrability of Hamiltonians with third and fourth degree polynomial potentials, B. Grammaticos, B. Dorizzi, A. Ramani J. Math. Phys., 24, 2289 (1983)
78. The effects of triaxial deformations on the structure of the 2+ transition charge density of 58Ni, B. Grammaticos, M. Girod, B. Frois et al., Phys. Lett. 122B, 347 (1983)
79. The cranked alpha particle model, E. Caurier, B. Grammaticos, Top. Meet. on Nucl. Fluid Dynamics, Trieste, 1982
80. The TDCM applied to the description of heavy-ion collisions, . Bauhoff, E. Caurier, B. Grammaticos, Top. Meet. on Nucl. Fluid Dynamics, Trieste, 1982
81. The "weak-Painleve" property and integrability of two-dimensional Hamiltonian systems, B. Grammaticos Invited lecture at the School of Non-linear Phenomena, Oaxtepec, Mexico,1982.
82. Integrals of motion for Toda systems with unequal masses, B. Dorizzi, B. Grammaticos, V. Papageorgiou, R. Padjen J. Math. Phys., 25, 2200 (1984)

83

83. On the nuclear curvature energy, B. Grammaticos, Zeit. Phys. A312, (1982)
84. La spectroscopie nucleaire comme test de l'interaction effective au delà de l'approximation Hartree-Fock M. Girod, B. Grammaticos, D. Gogny, VII session d'etudes de Phys. Nucl., Aussois,1983
85. Une classe d'Hamiltonien dependant du temps qui possedent un invariant exact B. Grammaticos, B. Dorizzi, R. Padjen, C.R. Acad. Sci. Paris 296 , 877 (1983)
86. The cranked cluster model for rapidly rotating light nuclei, E. Caurier, B. Grammaticos, Jour. Phys. G9, L125 (1983)
87. Chaos Quantique : un modele, Y. Pomeau, B. Dorizzi, B. Grammaticos, Contribution au Colloque de la SFP, Grenoble (1983)
88. Integrabilite de systemes dynamiques, B. Grammaticos, B. Dorizzi, A. Ramani, Contribution au Colloque de la SFP, Grenoble (1983)
89. Explicit Integrability for Hamiltonian systems and the Painleve conjecture, B. Dorizzi, B. Grammaticos, A. Ramani, J. Math. Phys. 25, 481 (1984)
90. Two-dimensional time-dependent Hamiltonian systems with an exact invariant, B. Grammaticos, B. Dorizzi, J. Math. Phys. 25, 2194 (1984)
91. Integrability and the Painleve property for low-dimensional systems, A. Ramani, B. Dorizzi, B. Grammaticos, T. Bountis J. Math. Phys. 25, 878 (1984)
92. The periodically kicked rotor : recurrence and/or energy growth, B. Dorizzi, B. Grammaticos, Y. Pomeau, J. Stat. Phys. 37, 93 (1984)
93. Hamiltonians with high order integrals and the "Weak Painleve" concept, B. Grammaticos, B. Dorizzi, A. Ramani, J. Math. Phys., 25, 3470 (1984)
94. Comment on "Painleve property of anharmonic systems with an external periodic field",A. Ramani, B. Dorizzi, B. Grammaticos Phys. Lett. 97A, 87 (1983)
95. Integrability of the Hirota-Satsuma equation: two tests, A. Ramani, B. Dorizzi, B. Grammaticos, Phys. Lett. 99A, 411 (1983)

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96. Sur l'integrabilite quantique des systemes Hamiltoniens classiquement integrables, J. Hietarinta, B. Dorizzi, B. Grammaticos, A. Ramani, C. R.Acad. Sci. Paris 297, 791 (1983)
97. On the complete and partial integrability of non Hamiltonian systems, T. Bountis, A. Ramani, B. Grammaticos, B. Dorizzi Physica A 128, 268 (1984)
98. On the quantization of the Kowalevskaya top, A. Ramani, B. Grammaticos, B. Dorizzi, Phys. Lett. 101A, 69 (1984)
99. Integrability of dynamical systems and the Painleve property, R. Padjen, B. Dorizzi, B. Grammaticos, A. Ramani Contr. to the Annual meeting of the American Physical Society (1984)
100. Solvable integrodifferential equations and their relation to the Painleve conjecture B. Grammaticos, B. Dorizzi, A. Ramani, Phys. Rev. Lett. 53 , 1 (1984)
101. Utilisation des techniques numeriques pour l'etude des systemes dynamiques B. Dorizzi, R. Padjen, C. Sebastien, B. Grammaticos, Note Technique CNET NT/PAA/TIM/MTI/1172
102. Quantification des systemes classiques Hamiltoniens independants du temps B. Dorizzi, A. Ramani, B. Grammaticos, Note Technique CNET NT/PAA/TIM/MTI/1174
103. A study of 24Mg (a,a') and 28Si (a,a') at 120 MeV using deformation dependent wave-functions C. Lagrange, M. Girod, B. Grammaticos, K. Kumar, Int. Conf. Nucl. Phys., Florence, 1983
104. Comment on "On the complete integrability of the Hirota-Satsuma system", A. Ramani, B. Dorizzi, B. Grammaticos, Jour. Phys. A. 18 , 1035 (1985)
105. Integrable Hamiltonian systems with velocity dep. potentials, B. Dorizzi, B. Grammaticos, A. Ramani, P. Winternitz, J. Math. Phys. 26 , 3070 (1985)
106. The Weak Painleve Property as criterion for the integrability of dynamical systems A. RaÒada, A. Ramani, B. Dorizzi, B. Grammaticos,J. Math. Phys. 26 , 708 (1985)
107. Extending integrable Hamiltonian systems from 2 to N dimensions B. Grammaticos, B. Dorizzi, A. Ramani, J. Hietarinta, Phys. Lett. 109A , 81 (1985)
108. Coupling constant metamorphosis and duality between integrable Hamiltonian systems J. Hietarinta, B. Grammaticos, B. Dorizzi, A. Ramani, Phys. Rev. Lett. 53 , 1707 (1984)

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109. Giant isoscalar resonances built on triaxial structures in nuclei, E. Caurier, M. Ploszajczak, B. Grammaticos, Phys. Lett. B151, 315 (1985)
110. Etude numerique de la propagation non-lineaire dans les fibres optiques, B. Dorizzi, R. Padjen, B. Grammaticos, Contribution à la RCP 759 (Dijon, 1984)
111. Complete Painleve analysis for coupled quartic oscillators in N dimensions, A. Ramani, B. Dorizzi, B. Grammaticos, J. Hietarinta, Phys. Lett. A108, 55 (1985)
112. Description of light ion collisions in TDCM model, W. Bauhoff, E. Caurier, B. Grammaticos, M. Ploszajczak,, Phys. Rev C32, 1915 (1985)
113. Linearization on a submanifold of integrable Hamiltonian with polynomial potentials A. Ramani, B. Dorizzi, B. Grammaticos, J. Hietarinta, Physica D18, 171 (1986)
114. Extended CC method for baryon scattering based on the dynamics of the Bohr Hamiltonian deduced from a microscopic nucleon-nucleon Hamiltonian, C. Lagrange, M. Girod, B. Grammaticos, K. Kumar, Phys. Rev C31, 762 (1985)
115. Soliton structure of the Drinfel'd-Sokolov-Wilson equation, R. Hirota, A. Ramani, B. Grammaticos, J. Math. Phys. 27, 1499 (1986)
116. Chaotic Rabi oscillations under quasiperiodic perturbations, Y. Pomeau, B. Dorizzi, B. Grammaticos, Phys. Rev. Lett. 56, 681 (1986)
117. Integrable curvilinear billiards, A. Ramani, A. Kalliterakis, B. Grammaticos, B. Dorizzi, Phys. Lett. A 115, 25 (1986)

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118. New integrable three-dimensional quartic potentials, B. Dorizzi, B. Grammaticos, J. Hietarinta, A. Ramani, F. Schwartz, Phys. Lett. A 116, 432 (1986)
119. Are all the equations of the Kadomtsev-Petviashvili hierarchy integrable ?, B. Dorizzi, B. Grammaticos, A. Ramani, P. Winternitz J. Math. Phys.27, 2848 (1986)
120. Linearisation et (non) integrabilite des equations de Yang-Mills, A. Ramani, B. Grammaticos, C.R. Acad. Sci. Paris 303 , 1417 (1986)
121. Comment on "Painleve test and integrability of nonlinear Klein-Fock-Gordon equations" , A. Ramani, B. Grammaticos, Jour. Phys. A 20 , 503 (1986)
122. Statistics and dimension of chaos in differential-delay systems, B. Dorizzi, B. Grammaticos , M. LeBerre, Y. Pomeau, E. Ressayre, A.Tallet, Phys. Rev. A35, 328 (1987)
123. Painleve resonances versus Kowalevski exponents: some exact results on singularity structure and integrability of dynamical systems, H. Yoshida, B. Grammaticos, A. Ramani, Acta Appl. Math. 8 (1987) 75
124. Quantum chaos with non-ergodic Hamiltonians, E. Caurier, B. Grammaticos, Europhys. Lett. 2 (1986) 417
125. A study of the statistics, time-scales and dimension of chaos in differential-delay systems, B. Grammaticos Contribution to the Conf. on Non-linear Dynamics and Chaos in Classical and Quantum Systems, Thessaloniki, 1986

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126. On the integrability of some generalised Toda lattices, H. Yoshida, J. Hietarinta, B. Grammaticos, A. Ramani, Physica A 144 (1987) 310
127. The demise of a good integrability candidate, B. Grammaticos, A. Ramani, H. Yoshida, Phys. Lett. 124 A (1987) 65
128. On the non- integrability of a class of Hamiltonian systems, J. Hietarinta, H. Yoshida, A. Ramani, B. Grammaticos, Europhys. Lett. 5 (1988) 195
129. Structural stability of the KdV soliton under a singular perturbation Y. Pomeau, A. Ramani, B. Grammaticos, Physica D 31 (1988) 127
130. Integrable bouncing-ball models, B. Grammaticos, V. Papageorgiou, Phys. Rev. A 37 (1988) 5000
131. Non-integrability of the fourth-order truncated Toda Hamiltonian, H. Yoshida, A. Ramani, B. Grammaticos,Physica D 30 (1988) 151
132. Comment on "Singular point analysis, ä", A. Ramani, B. Grammaticos,H. Yoshida, Jour. Phys. A : Math. Gen. 21 (1988) 1471
133. The Painleve property and singularity analysis of integrable and non-integrable systems, A. Ramani, B. Grammaticos, T. Bountis Physics Reports 180 (1989) 159

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134. Extreme level repulsion for chaotic quantum Hamiltonians, E. Caurier, B. Grammaticos, Phys. Lett. A 136 (1989) 387
135. Rigorous non-integrability results related to singularity analysis, A. Ramani, B. Grammaticos, H. Yoshida "Non-linear Evolution Equations: Integrability and Spectral Methods", Manchester Univ. Press (1990) 193
136. Lie Symmetries of a Generalized Nonlinear Schrˆdinger Equation : Reductions to 3rd order ODE's L. Gagnon, B. Grammaticos, A. Ramani, P. Winternitz, Jour. Phys. A: Math. Gen. 22 (1989) 499
137. On the h-bar-square correction terms in quantum integrability, J. Hietarinta, B. Grammaticos, Jour. Phys. A: Math. Gen. 22 (1989) 1315
138. Integrals of quadratic ODE's in R3: the Lotka-Volterra system B. Grammaticos, J. Moulin-Ollagnier, A. Ramani, J.M. Strelcyn, S. Wojciechowski, Physica A 163 (1990) 683
139. Electron scattering studies of the ground state rotational band of 152Sm B. Grammaticos, X.H. Phan et al., Physical Review C 38 (1988) 1173

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140. Why some integrable (2-D) Hamiltonians cannot be extended to higher dimensions, B. Grammaticos, A. Ramani, Phys. Lett. A 139 (1989) 299
141. Singularity analysis and its relation to complete, partial and non-integrability, M. D. Kruskal, A. Ramani, B. Grammaticos Course given at the Les Houches '89 School on, Partially Integrable Nonlinear Evolution Equations
142. Mathematical methods for integrability, B. Grammaticos, Course given at the Samos 89 Summer school of Nonlinear Physics
143. Comment on the article : "Integrable potentials with logarithmic integrals of motion" by Ichtiaroglou and Voyatzis, B. Grammaticos and A. Ramani, J. Phys. A : Math. Gen. 23 (1990) 3095

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144. A search for integrable bilinear equations: the Painleve approach, B. Grammaticos, A. Ramani and J. Hietarinta, J. Math. Phys. 31 (1990) 2572
145. Level repulsion near integrability: a random matrix analogy, E. Caurier, B. Grammaticos, A. Ramani, Jour. Phys. A 23 (1990) 4903
146. A model for the synchronisation of neuronal oscillations, B. Grammaticos, B. Dorizzi, Europhys. Lett. 14 (1991) 169
147. Painleve integrability: theorems and conjectures, B. Grammaticos, A. Ramani Painleve transcendents, (Montreal 1990), Levi and Winternitz eds., NATO ASI B 278, Plenum (1992), p. 145
148. Level spacing for band random matrices, B. Grammaticos, A. Ramani, E. Caurier Jour. Phys. A 23 (1990) 5855
149. Lie symmetries for Hirota's bilinear equations, K. M. Tamizhmani, A. Ramani, B. Grammaticos, Jour. Math. Phys. 32 (1991) 2635
150. Integrable higher Nonlinear Schrˆdinger equations, B. Grammaticos, A. Ramani, Solitons and Chaos, (Bruxelles 1990) Antoniou, Lambert eds., Springer 1992, p. 243

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151. Delay induced desynchronisation in neuronal oscillations, B. Dorizzi, B. Grammaticos, Phys. Rev. A 44 (1991) 6958
152. The mKdV with one-half degree of nonlinearity is not integrable (comment on a paper by Yi Xiao) A. Ramani, B. Grammaticos, Jour. Phys. A: Math. Gen. 24 (1991) 1969
153. Stimulus-induced neural synchronisations, B. Dorizzi, B. Grammaticos, Contribution to the ICANN-91
154. Do integrable mappings have the Painleve, property?, B. Grammaticos, A. Ramani, V. Papageorgiou, Phys. Rev. Lett. 67 (1991) 1825
155. Discrete versions of the Painleve equations, A. Ramani, B. Grammaticos, J. Hietarinta, Phys. Rev. Lett. 67 (1991) 1829
156. Linearizable mappings, A. Ramani, B. Grammaticos, G. Karra, Physica A 180 (1992) 115
157. Integrability of discrete-time systems, B. Grammaticos, G. Karra, A. Ramani, V. Papageorgiou "Chaotic Dynamics: Theory and Practice " T. Bountis ed., Plenum (1992), p. 75

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158. Synchronisation of coupled oscillations: an analysis of the comparator model, B. Grammaticos, B. Dorizzi,Jour. Phys. A 25 (1992) L701
159. Miura transforms for discrete Painleve equations, A. Ramani, B. Grammaticos, Jour. Phys. A 25 (1992) L633
160. Isomonodromic deformation problems for discrete analogues of Painleve equations V. Papageorgiou, F. Nijhoff, B. Grammaticos, A. Ramani, Phys. Lett. A 164 (1992) 57
161. From continuous to discrete Painleve equations, A Fokas, B. Grammaticos, A. Ramani, J. of Math. Anal. and Appl. 180 (1993) 342
162. Quantization and integrability of discrete systems, B. Grammaticos, A. Ramani, V. Papageorgiou, F. Nijhoff, Jour. Phys. A 25 (1992) 6419
163. An integrability test for differential-difference systems, A. Ramani, B. Grammaticos, K. M. Tamizhmani, Jour. Phys. A 25 (1992) L883
164. Painleve analysis and singularity confinement: the ultimate conjecture, A. Ramani, B. Grammaticos, K. M. Tamizhmani, Jour. Phys. A 26 (1993) L53
165. Integrability of multidimensional discrete systems, A. Ramani, B. Grammaticos, J. Satsuma, Phys. Lett. A 169 (1992) 323
166. Discrete Painleve equations: derivation and properties, B. Grammaticos, A. Ramani, NATO ASI C413, Plenum 1992, p. 299
167. A bilinear approach to integrable lattices and their similarity reductions, J. Satsuma, A. Ramani, B. Grammaticos, Phys. Lett. A 174 (1993) 387
168. Integrability in continuous and discrete dynamical systems, B. Grammaticos Invited talk to the Hellenic Astronomy Conference, Athens, 1992. (Praktika s. 407).
169. Delay differential equations and the Painleve transcendents, B. Grammaticos, A. Ramani, I. Moreira, Physica A 196 (1993) 574

93

170. Integrable lattices and convergence acceleration algorithms, V. Papageorgiou, B. Grammaticos, A. Ramani, Phys. Lett. A 179 (1993) 111
171. Painleve analysis for the Mixmaster universe model, G. Contopoulos, B. Grammaticos, A. Ramani, Jour. Phys. A26 (1993) 5795
172. Logarithmic terms in the spectral statistics of band random matrices, E. Caurier, A. Ramani, B. Grammaticos, Jour. Phys. A 26 (1993) 3845
173. Investigating the integrability of discrete systems, B. Grammaticos, A. Ramani, Int. J. of Mod. Phys. B 7 (1993) 3551
174. Schlesinger transforms for the discrete Painleve-IV equation, K. M. Tamizhmani, B. Grammaticos, A. Ramani, Lett. Math. Phys. 29 (1993) 49
175. Nonproliferation of preimages in integrable mappings, B. Grammaticos, A. Ramani, K. M. Tamizhmani, Jour. Phys. A 27 (1994) 559
176. Linearization and solution of the discrete Painleve- III equation, B. Grammaticos, F.W. Nijhoff, V.Papageorgiou, A. Ramani, J. Satsuma, Phys. Lett. A 185 (1994) 446
177. Quantum Hamiltonians from level statistics via dressing transformations, A. Ramani, B. Grammaticos, E. Caurier, J. Math. Comp. in Sim. 37 (1994) 451
178. Integrable discrete systems and numerical integrators, B. Grammaticos, B. Dorizzi, J. Math. Comp. in Sim. 37 (1994) 341
179. Casorati determinant solutions for the discrete Painleve -II equation, K. Kajiwara, Y. Ohta, J. Satsuma, B. Grammaticos, A. Ramani, Jour. Phys. A 27 (1994) 915
180. Generalized separability for a Hamiltonian with a nonseparable quartic potential, V. Ravoson, A. Ramani, B. Grammaticos Phys. Lett. A 191 (1994) 91
181. Integrability of the Mixmaster Universe, G. Contopoulos, B. Grammaticos, A. Ramani, Proc. "Chaos in relativity" , Plenum 1994, p. 423
182. Continuous vacua in bilinear soliton equations, J. Hietarinta, A. Ramani, B. Grammaticos, Jour. Phys. A 27 (1994) 3149
183. Electromagnetic properties of fractal aggregates and composite systems B. Grammaticos, A. Ramani, T. Robin, M. Rosso, B. Souillard, Rapport X-RS, 93

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184. Fractal potentials from energy levels, A. Ramani, B. Grammaticos, E. Caurier, Phys. Rev E 51 (1995) 6323
185. The Mixmaster Universe Model, revisited, G. Contopoulos, B. Grammaticos, A. Ramani, Jour. Phys. A 27 (1994) 5357
186. Orthogonal polynomial approach to discrete Lax pairs for initial-boundary value problems of the QD algorithm V. Papageorgiou, B. Grammaticos, A. Ramani, Lett. Math. Phys. 34 (1995) 91
187. Multilinear operators: the natural extension of Hirota's bilinear formalism, B. Grammaticos, J. Hietarinta, A. Ramani,Phys. Lett. A 190 (1994) 6
188. Continuous and semi-discrete trilinear equations: investigating their integrability, J. Satsuma, B. Grammaticos, A. Ramani, RIMS Kokyuroku 868 (1994) 129
189. Coalescence of singularities and Ziglin's approach to nonintegrability, A. Ramani, B. Grammaticos,V. Ravoson, Phys. Lett A 199 (1995) 327
190. Singularity confinement, B. Grammaticos, A. Ramani, V. Papageorgiou, CRM Lecture Notes 9 (1996) 303
191. Integrable mappings from matrix transformations and their singularity properties A. Ramani, B. Grammaticos, J-M. Maillard, G. Rollet, J. Phys. A 27 (1994) 7597
192. Integrable trilinear PDE's, J. Hietarinta, A. Ramani, B. Grammaticos, Proceedings of the NEEDS '94 (Los Alamos)
193. KdV equations and integrability detectors, B. Grammaticos, V. Papageorgiou, A. Ramani, Acta Appl. Math. 39 (1995) 335
194. Integrable difference equations and numerical analysis algorithms, V. Papageorgiou, B. Grammaticos, A. Ramani, CRM Lecture Notes 9 (1996) 269
195. Bilinear discrete Painleve-II and its particular solutions, J. Satsuma, K. Kajiwara, B. Grammaticos, J. Hietarinta, A. Ramani Jour. Phys. A 28 (1995) 3541

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196. Bilinear discrete Painleve equations, A. Ramani, B. Grammaticos, J. Satsuma, Jour. Phys. A 28 (1995) 4655
197. The last remake of the Mixmaster Universe Model, G. Contopoulos, B. Grammaticos, A. Ramani, Jour. Phys. A 28 (1995) 5313
198. The Gambier Mapping, B. Grammaticos, A. Ramani, Physica A 223 (1995) 125
199. Discrete Painleve equations: coalescences, limits and degeneracies, A. Ramani, B. Grammaticos, Physica A 228 (1996) 160
200. Retracing the Painleve-Gambier classification for discrete systems, B. Grammaticos, A. Ramani, Meth. and Appl. of An. 4 (1997) 196
201. A study of the discrete PV equation: Miura transforrmations and particular solutions, K.M. Tamizhmani, A. Ramani, B. Grammaticos,Y. Ohta, Lett. Math. Phys. 38 (1996) 289
202. From discrete to continuous Painleve equations: a bilinear approach, Y. Ohta, A. Ramani, B. Grammaticos, K.M. Tamizhmani, Phys. Lett. A 216 (1996) 255
203. A study of the alternate discrete Painleve-II equation, F. Nijhoff, J. Satsuma, K. Kajiwara, B. Grammaticos, A. Ramani, Inv. Probl. 12 (1996) 697-716
204. Bilinear structure and Schlesinger transforms of the q-PIII and q-PVI equations, M. Jimbo, H. Sakai, A. Ramani, B. Grammaticos, Phys. Lett. A 217 (1996) 111

96

205. Integrability (and how to detect it), B. Grammaticos, A. Ramani, Course at the Pondicherry 96 school, Springer LNP 495 (1997) 30
206. Cellular automata and ultra-discrete Painleve equations, B. Grammaticos, Y. Ohta, A. Ramani, D. Takahashi, K.M. Tamizhmani, Phys. Lett. A 226 (1997) 53
207. The Painleve of discrete equations and other stories, A. Ramani, B. Grammaticos, Y. Ohta, invited talk at the Montreal 96 conference.
208. Discrete Painleve equations, B. Grammaticos, F. Nijhoff, A. Ramani, CRM Series in Mathematical Physics, Ed. R. Conte, Springer-Verlag, New-York (1999) 413.
209. A Miura of the Painleve I equation and its discrete analogs, B. Grammaticos, Y. Ohta, A. Ramani, J. Satsuma, K.M. Tamizhmani, Lett. Math. Phys. 39 (1997) 179
210. Painleve equations and cellular automata, B. Grammaticos, A. Ramani, LMS Lecture Notes 255, Ed. P. Clarkson and F. Nijhoff, Cambridge Univ. Press (1999) 325.
211. The ultimate discretisation of the Painleve equations, B. Grammaticos, Y. Ohta, A. Ramani, D. Takahashi, Physica D 114 (1998) 185
212. Singularity confinement analysis of integrodifferential equations of Benjamin-Ono type, K.M. Tamizhmani, A. Ramani, B. Grammaticos, J. Phys. A 30 (1997) 1017
213. From integrability to chaos in a cellular-automaton Lotka-Volterra equation, R. Hirota, K. Iwao, A. Ramani, D. Takahashi, B. Grammaticos, Y. Ohta, Phys Lett A 236 (1997) 39
214. Toda equations and the Painleve property, B. Grammaticos, A. Ramani, Lecture at the Toda 96 symposium
215. The Grand Scheme for discrete Painleve equations, A. Ramani, B. Grammaticos, Lecture at the Toda 96 symposium
216. Self-duality and Schlesinger chains for the, asymmetric d-PII and q-PIII equations, A. Ramani, Y. Ohta, J. Satsuma, B. Grammaticos, Comm. Math. Phys. 192 (1998) 67

97

217. Continuous and discrete linearisable systems: the Riccati saga, B. Grammaticos, A. Ramani, in Algebraic Methods in Physics, Y. Saint-Aubin and L. Vinet eds., Springer CRM Series (2001) 81
218. Discretising families of linearisable equations, B. Grammaticos, A. Ramani, P. Winternitz, Phys. Lett. A 245 (1998) 382
219. Discrete dressing transformations and Painleve equations, B. Grammaticos, A. Ramani, V. Papageorgiou, Phys. Lett. A 235 (1997) 475
220. Constructing solutions to the ultra-discrete Painleve equations, D. Takahashi, T. Tokihiro, B. Grammaticos, Y. Ohta, A. Ramani, J. Phys. A. 30 (1997) 7953
221. Constructing integrable third-order systems: the Gambier approach, S. Lafortune, B. Grammaticos, A. Ramani, Inv. Prob. 14 (1998) 287
222. Again, linearisable mappings, A. Ramani, B. Grammaticos, K.M. Tamizhmani, S. Lafortune, Physica A 252 (1998) 138
223. Degeneration through coalescence of the q-Painleve VI equation, B. Grammaticos, Y. Ohta, A. Ramani, H. Sakai, J. Phys. A 31 (1998) 3545
224. Microwave permeability of ferrite loaded composites: comparison between model and experiment, J.P. Ganne, M. Pate, B. Grammaticos, A. Ramani and T. Robin, J. Phys IV France 7 (1997) C1-429
225. The Gambier Mapping revisited, B. Grammaticos, A. Ramani, S. Lafortune Physica A 253 (1998) 260
226. Integrability in a discrete world, B. Grammaticos and A. Ramani, Chaos, Solitons and Fractals 11 (2000) 7.
227. Coalescence cascades and special function solutions for the continuous and discrete Painleve equations, K.M. Tamizhmani, A. Ramani, B. Grammaticos, K. Kajiwara J. Phys. A 31 (1998) 5799

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228. Singularity confinement and Symmetries of Differential-Difference KP equation, K.M. Tamizhmani, S. KanagaVel, B. Grammaticos, A. Ramani, contribution to the Tiruchirapali 1998 Conference on Integrability and chaos in dynamical systems, Narosa Ed. (2000) 211.
229. Integrability and chaos in discrete and ultradiscrete systems, B.Grammaticos, A.Ramani, O.Gerard, in:Nonlinear dynamics:integrability and chaos, eds. M.Daniel, K.M.Tamizhmani, R.Sahadevan (Narosa, New Delhi, 2000) p.163.
230. From continuous Painleve IV to the asymmetric discrete Painleve I, B. Grammaticos A. Ramani, J. Phys. A 31 (1998) 5787
231. A bilinear approach to discrete Miura transformations, N. Joshi, A. Ramani, B. Grammaticos, Phys. Lett. A 249 (1998) 59
232. A study of the continuous and discrete Gambier system, A. Ramani, B. Grammaticos, S. Lafortune, CRM Proceedings and Lecture Notes v 25. (2000) 367.
233. Singularity Structure and Algebraic Properties of the Differential-Difference Kadomstev-Petviashvili Equation, K.M. Tamizhmani, S. KanagaVel, B. Grammaticos, A. Ramani, Chaos, Solitons and Franctals 11 (2000) 1423.
234. Schlesinger transformations for linearisable equations, A. Ramani, B. Grammaticos, S. Lafortune, Lett. Math. Phys. 46 (1998) 131.
235. Deautonomisation of differential-difference equations and discrete Painleve equations, B. Grammaticos, A. Ramani, K.M. Tamizhmani, Chaos, Solitons & Fractals 11 (2000) 757.
236. Linearizable systems and the Gambier approach, S. Lafortune, A. Ramani, B. Grammaticos, CRM Proceedings and Lecture Notes v 25. (2000) 255..
237. Asymmetric discrete Painleve equations, M.D. Kruskal, K.M. Tamizhmani, B. Grammaticos, A. Ramani, Reg. Chaot. Dyn. 5, N∞3 (2000) 273.
238. On Discrete Painleve Equations Associated with the Lattice KdV Systems and the Painleve VI Equation, F.W. Nijhoff, A. Ramani, B.Grammaticos, Y. Ohta, Stud. Appl. Math. 106, (2000) 261.
239. Special functions solutions for asymmetric discrete Painleve equations, T. Tamizhmani , K. M. Tamizhmani, B. Grammaticos, A. Ramani, J. Phys. A 32 (1999) 4553.
240. Discrete and Continuous Linearizable Equations, S. Lafortune, B. Grammaticos, A. Ramani, Physica A 268 (1999) 129.
241. Nonlinear Integrodifferential Equations as Discrete Systems, K. M. Tamizhmani, J. Satsuma, B. Grammaticos, A. Ramani, Inv. Prob. 15 (1999) 787.

99

242. On a q-discrete analogue of the Painleve VI equation, B. Grammaticos, A. Ramani, Phys. Lett. A 257 (1999) 288.
243. On a transcendental equation related to Painleve III equation and its discrete forms, A. Ramani, B. Grammaticos, T. Tamizhmani, K.M. Tamizhmani, J. Phys. A 33 (2000) 579.
244. Singularity confinement and algebraic entropy: the case of the discrete Painleve equations, Y. Ohta, K.M. Tamizhmani, B. Grammaticos, A. Ramani, Phys. Lett. A 262 (1999) 152.
245. Integrability criteria for differential-difference systems: a comparison of singularity confinement and low-growth requirements, K.M. Tamizhmani, A. Ramani, B. Grammaticos, Y. Ohta, J. Phys. A 32 (1999) 6679.
246. Linearisable mappings and the low-growth criterion, A. Ramani, B. Grammaticos, S. Lafortune, Y. Ohta, J. Phys. A 33 (2000) L287.
247. Blending two discrete integrability criteria: singularity confinement and algebraic entropy, S. Lafortune, A. Ramani, B. Grammaticos, Y. Ohta, K.M. Tamizhmani, CRM proceedings Vol 29 (2001) p.299.
248. The hunting for the discrete Painleve equations, B. Grammaticos, A. Ramani, Reg. and Chaot. Dyn., 5 (2000) 53.
249. Discrete integrable systems from continuous Painleve equations through limiting procedures, A. Ramani, B. Grammaticos, Y. Ohta, B. Grammaticos, Nonlinearity 13 (2000) 1073.
250. Discrete systems related to some equations in the Painleve-Gambier classification, S. Lafortune, B. Grammaticos, A. Ramani, P. Winternitz, Phys. Lett. A 270 (2000) 55.
251. Integrable lattice equations and their growth properties, S. Tremblay, B. Grammaticos, A. Ramani, Phys. Lett. A 278 (2001) 319.
252. A geometrical description of the discrete Painleve VI and V equations, A. Ramani, B. Grammaticos, Y. Ohta, Comm. Math. Phys. 217 (2001) 315.
253. Quadratic relations in continuous and discrete Painleve equations, A. Ramani, B. Grammaticos, T. Tamizhmani, J. Phys. A 33 (2000) 3033

00

254. Integrable systems without the Painleve property, A. Ramani, B. Grammaticos, S. Tremblay, J. Phys. A 33 (2000) 3045
255. Special function solutions of the discrete Painleve equations, A. Ramani, B. Grammaticos, K.M. Tamizhmani, T. Tamizhmani, to appear in Intl. J. on Comp. and Math. 42, (2001) 603
256. What is the discrete analogue of the Painleve property?, A. Ramani, B. Grammaticos, contribution to the Kruskal 2000 festschrift, ANZIAM Journal 44 (2002) 21
257. The q-Painleve V equation and its geometrical description, A. Ramani, B. Grammaticos and Y. Ohta, J. Phys. A 34 (2001) 2505
258. Special relations for continuous and discrete Painleve equations, A. Ramani, B. Grammaticos and T. Tamizhmani, J. Phys. A 33 (2000) L415
259. Bilinear forms of continuous and discrete Painleve equations, B. Grammaticos, Y. Ohta, A. Ramani, J. Satsuma and K.M. Tamizhmani, to appear in the monograph on Hirota Bilinear Forms, F. Lambert editor
260. On a class of special solutions of the Panleve equations, T. Tamizhmani, B. Grammaticos, A. Ramani, and K.M. Tamizhmani, Physica A 295 (2001) 359
261. Who cares about the Painleve property?, B. Grammaticos, A. Ramani, S. Tremblay, S. Lafortune, invited talk at the SIDE IV conference, (Tokyo, 2000)
262. Growth and Integrability in discrete systems, B. Grammaticos, T. Tamizhmani, A. Ramani, and K.M. Tamizhmani, J. Phys A 34 (2001) 3811

01

263. On the road to the discrete analogue of the Painleve property: Nevanlinna meets singularity confinement, B. Grammaticos, T. Tamizhmani, A. Ramani and K.M. Tamizhmani, Intl. J. on Comp. and Math. 45 (2003) 1001
264. An affine Weyl group approach to the 8-parameter discrete Painleve equations, Y. Ohta, A. Ramani, B. Grammaticos, J. Phys. A 34 (2001) 10523.
265. A Nevanlinna theory approach to the integrability of discrete systems, T. Tamizhmani, B. Grammaticos, A. Ramani and K.M. Tamizhmani, , in Nonlinear Systems, Ed. T. Sahadevan, Narosa 2002, p. 297.
266. A panorama of the special solutions of the Painleve equations, K.M. Tamizhmani, B. Grammaticos, A. Ramani and T. Tamizhmani, , in Nonlinear Systems, Ed. T. Sahadevan, Narosa 2002, p. 265.
267. Constructing the soliton solutions of the N=1 supersymmetric KdV hierarchy, S. Carstea, A. Ramani and B. Grammaticos, Nonlinearity 14 (2001) 1419
268. Bilinearisation and soliton solutions of the N=1 supersymmetric sine-Gordon equation, B. Grammaticos, A. Ramani and S. Carstea, J. Phys. A 34 (2001) 4881
269. A unified description of the asymmetric q-PV and d-PIV equations and the Schlesinger transformations, B. Grammaticos, A. Ramani and Y. Ohta, to appear in J. Non. Math. Phys. 10 (2003) 215
270. Fermionic extensions of Painleve equations, A. Ramani, S. Carstea and B. Grammaticos, Phys. Lett. A 292 (2001)115
271. On the autonomous limit of discrete Painleve equations, A. Ramani, S. Carstea, B. Grammaticos and Y. Ohta, Physica A 305 (2002) 437.
272. Linearisable supersymmetric equations, S. Carstea, A. Ramani and B. Grammaticos, Chaos Solitons and Fractals 14 (2002) 155
273. A bilinear approach to the discrete Painleve I equations, B. Grammaticos, T. Tamizhmani, A. Ramani, A. S. Carstea and K.M.Tamizhmani, J. Phys. Soc. Japan 71 (2002) 443.
274. A new class of integrable discrete systems, K. Kimura, H. Yahagi, R. Hirota, A. Ramani, B. Grammaticos and Y. Ohta, J. Phys. A 35 (2002) 9205
275. Integrable third-order mappings and their growth properties, S. Lafortune, S. Carstea, A. Ramani, B. Grammaticos and Y. Ohta, Reg. Chaot. Dyn. 6 (2001) 443.

02

276. Supersymmetric soliton equations, A. Ramani, S. Carstea and B. Grammaticos, Proceedings of the Kyushu 2001 workshop, 13ME-S4 (2002) 36
277. From continuous PV to discrete Painleve equations, T. Tokihiro, B. Grammaticos, A. Ramani, J. Phys. A 35 (2002) 5943
278. Special solutions of discrete Painleve equations through direct linearisation, T. Tamizhmani, B. Grammaticos, A. Ramani and K.M. Tamizhmani, Physica A 315 (2002) 569
279. The discrete Chazy III system of Labrunie-Conte is not integrable, A. Ramani, B. Grammaticos, S. Lafortune, J. Phys. A 35 (2002) 7943
280. The space of initial conditions for linearisable mappings, T. Takenawa, M. Eguchi, B. Grammaticos, Y. Ohta,A. Ramani and J. Satsuma, Nonlinearity 16 (2003) 457
281. The last remake of the Gambier mapping, S. Lafortune, A. Ramani, B. Grammaticos, Physica A 317 (2003) 383
282. Discrete Integrability, K.M. Tamizhmani, B. Grammaticos, A. Ramani and T. Tamizhmani, in Classical and Quantum Integrable Systems (IOP Publishing), ed. A. Kundu, (2003) p64
283. Elliptic discrete Painleve equations, Y. Ohta, A. Ramani, B. Grammaticos, J. Phys. A 35 (2002) L653.
284. The extension of integrable mappings to non-commuting variables, T. Tamizhmani, B. Grammaticos, A. Ramani and K.M. Tamizhmani, J. Nonlin. Math. Phys. 10, supp 2 (2003) 149
285. Special functions as solutions to discrete Painleve equations, K.M. Tamizhmani, B. Grammaticos, A. Ramani and T. Tamizhmani, J. Comp. Appl. Math. 160 (2003) 307.
286. Similarity reductions of Hirota bilinear equations and Painleve equations, , K.M. Tamizhmani, B. Grammaticos, A. Ramani, Y. Ohta and T. Tamizhmani, NATO Science Series II: Mathematics, Physics and Chemistry , Vol. 201, Faddeev, Ludwig; Van Moerbeke, Pierre; Lambert, Franklin (Eds.) p. 313
287. Bilinear avatars of the discrete Painleve II equation, B. Grammaticos, A. Ramani and A.S. Carstea, NATO Science Series II: Mathematics, Physics and Chemistry , Vol. 201, Faddeev, Ludwig; Van Moerbeke, Pierre; Lambert, Franklin (Eds.) p. 85

03

288. On the integrability of correspondences associated to integral curves, C.M. Viallet, A. Ramani and B. Grammaticos Phys. Lett. A 322 (2004) 186
289. Epidemic dynamics: discrete-time and cellular automaton models, R. Willox, B. Grammaticos, A.S. Carstea and A. Ramani, Physica A 328 (2203) 13
290. The discrete Painleve II equations: Miura and auto-Backlund transformations, A.S. Carstea, A. Ramani, R. Willox and B. Grammaticos, J. Phys. A 36 (2003) 8419
291. The q-PIV equations and their properties, K.M. Tamizhmani, B. Grammaticos, A.S. Carstea and A. Ramani, Reg. Chao. Dyn. 9 (2004) 13
292. Oscillating epidemics: a discrete-time model, A. Ramani, A.S. Carstea, R. Willox and B. Grammaticos, Physica A 333 (2204) 278
293. Solvable chaos, B. Grammaticos, A. Ramani and C.M. Viallet, Phys. Lett. A 336 (2005) 152
294. Integrability (and how to detect it), B. Grammaticos, A. Ramani, Course at the CIMPA, Pondicherry School (2003), Springer LNP 644 (2004) 245
295. Special solutions for discrete Painleve equations, K.M. Tamizhmlani, T. Tamizhmani, B. Grammaticos, A. Ramani, Course at the CIMPA, Pondicherry School (2003) Springer LNP 644 (2004) 323
296. Extending the SIR epidemic model, J. Satsuma, R. Willox, A. Ramani, A.S. Carstea, B. Grammaticos, Physica A 336 (2004) 369

04

297. Modelling AIDS epidemic and treatment with difference equations, K.M. Tamizhmani, A. Ramani, B. Grammaticos. A.S. Carstea, Adv. Diff. Eq. 3 (2004) 183.
298. Supersymmetry and Integrability, A.S. Carstea, A. Ramani; B. Grammaticos, Romanian J. of Phys. 47 (2002) 383
299. Three lessons on the Painleve property and the Painleve equations, M.D. Kruskal, B. Grammaticos, T. Tamizhmani, Course at the CIMPA, Pondicherry School (2003), Springer LNP 644 (2004) 1
300. On the discrete form of the Fokas-Ablowitz equation, A. Ramani and B. Grammaticos, Chaos Sol. Frac. 24 (2005) 1331.
301. Reductions of integrable lattices, B. Grammaticos, A. Ramani, J. Satsuma,R. Willox, A.S. Carstea, J. Nonlin. Math. Phys. 12, supp 1 (2005) 363
302. Limits and degeneracies of discrete Painleve equations, A. Ramani, R. Willox, B. Grammaticos, A.S. Carstea, J. Satsuma, Physica A 347 (2005) 1.
303. On the alternate discrete Painleve equations and related systems, A. Ramani, B. Grammaticos, T. Tamizhmani, Seminaires et Congres de la SMF 14 (2006) 205
304. Generating discrete Painleve equations from affine Weyl groups, B. Grammaticos, A. Ramani Reg. Chao. Dyn. 10 (2005) 145.

05

305. Integrable mappings with transcendental invariants, B. Grammaticos, A. Ramani, Communications in Nonlinear Science and Numerical Simulation 17 (2007) 350
306. A study of the antisymmetric QRT mappings, R. Willox, B. Grammaticos, A. Ramani to appear in J. Phys. A 38 (2005) 5227
307. Continuous, discrete and ultradiscrete models of an inflammatory response, A.S. Carstea, A. Ramani, J. Satsuma, R. Willox, B. Grammaticos, Physica A 364 (2006) 276
308. Alternate discrete Painleve equations from limits of q-PVI and d-PV, T. Tamizhmani, B. Grammaticos, A. Ramani and K.M. Tamizhmani, Physica A 369 (2006) 463
309. On the identity of two q-discrete Painleve equations and their geometrical derivation, B. Grammaticos, A. Ramani, T. Takenawa, Adv. Diff. Eq. 2006 (2006) 36397
310. Painleve equations: from continuous to discrete, K. M. Tamizhmani, B. Grammaticos, A. Ramani, T. Tamizhmani, Proc.Nat.Acd.Sci.India Sect. A.Vol.78, Pt.II (2008) 85
311. On the dynamics of a gene regulatory network, B. Grammaticos, S. Carstea, A. Ramani, J. Phys. A 39 (2006) 2965
312. Deconstructing an integrable lattice equation, A. Ramani, N. Joshi, B. Grammaticos, T. Tamizhmani, J. Phys. A 39 (2006) L145.
313. A cellular automaton model for the migration of glioma cells, M. Aubert, M. Badoual, S. Fereol, C. Christov, B. Grammaticos, Phys. Biol. 3 (2006) 93

06

314. Ultradiscretisation without positivity, S. Isojima, B. Grammaticos, A. Ramani, J. Satsuma, J. Phys. A 39 (2006) 3663
315. From integrable lattices to non-QRT mappings, N. Joshi, B. Grammaticos, T. Tamizhmani, A. Ramani, Lett. Math. Phys. 78 (2006) 27
316. Discrete systems related to the sixth Painleve equation, A. Ramani, Y. Ohta, B. Grammaticos, J. Phys. A 39 (2006) 12167
317. Nonintegrability of (2+1)-dimensional continuum isotropic Heisenberg spin system: Painleve analysis, C. Senthil Kumar, M. Lakshmanan, B. Grammaticos, A. Ramani, Phys. Lett. A 356 (2006) 339
318. Modelling the dynamics of nonendemic epidemics, A. Ramani, B. Grammaticos, J. Satsuma, Chaos, Solitons and Fractals 40 (2009) 491
319. Eigenproblem of large powers of the Laplacian in bounded domains, A. Ramani, B. Grammaticos, Y. Pomeau, J. Phys. A, 40 (2007) F391
320. Analysis of a minimal model for p53 oscillations, S. Bottani, B. Grammaticos, J. Theor. Biol. 249 (2007) 235
321. The physical basis of scoring the athletic performance, B. Grammaticos, New Stud. Athl. 22 (2007) 47
322. An (almost) solvable model for bacterial pattern formation, M. Badoual, B. Grammaticos, M. Aubert, in Physica D 234 (2007) 90

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323. A simple model of genetic oscillations through regulated degradation, S. Bottani, B. Grammaticos, Chaos, Solitons and Fractals 38 (2008) 1468
324. Constructing lump-like solutions of the Hirota-Miwa equation, B. Grammaticos, V. Papageorgiou, A. Ramani, J. Satsuma, R. Willox, J. Phys. A 40 (2007) 12619
325. A model for glioma cell migration on collagen and astrocytes, M. Aubert, M. Badoual, C. Christov, B. Grammaticos, Proc. Roy. Soc. Interface 5 (2008) 7583
326. From limit cycles to periodic orbits through ultradiscretisation, R. Willox, A. Ramani, J. Satsuma, B. Grammaticos, Physica A 385 (2007) 473
327. A class of integrable and nonintegrable mappings and their dynamics, T. Tsuda, A. Ramani, B. Grammaticos, T. Takenawa, Lett. Math. Phys. 82 (2007) 39
328. Do integrable cellular automata have the confinement property?, B. Grammaticos, A. Ramani, K.M. Tamizhmani, T. Tamizhmani, A.S. Carstea, J. Phys. A. 40 (2007) F725
329. Proteomic signals in simple transcriptional cascades, A.S. Carstea, A. Ramani, K.M. Tamizhmani, B. Grammaticos, Chaos, Solitons and Fractals 41 (2009) 1823
330. Do all integrable evolution equations have the Painleve property?, K.M. Tamizhmani, A. Ramani, B. Grammaticos, SIGMA 3 (2007) 73
331. Quantum Painleve equations: from continuous to discrete, H. Nagoya, B. Grammaticos, A. Ramani, SIGMA 4 (2008) 51
332. Toda equations as paradigms of integrable (continuous, discrete and ultradiscrete) systems, B. Grammaticos, A. Ramani, Reports of the RIAM Symposium (2007) 69.
333. Do all integrable equations satisfy integrability criteria? B. Grammaticos, A. Ramani, K.M. Tamizhmani, T. Tamizhmani, A.S. Carstea, Adv. Diff. Eq. 2008 (2008) 317520

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334. Bilinearisation and solutions of the KdV6 equation, A. Ramani, B. Grammaticos, R. Willox, Anal. and Appl. 6 (2008) 401
335. Discretisation induced delays and their role in the dynamics, A. Ramani, B. Grammaticos, J. Satsuma, R. Willox, J. Phys. A 41 (2008) 205204
336. A model for short- and long-range interaction of migrating tumour cells, M. Aubert, M. Badoual, B. Grammaticos, Acta Biotheor. 56 (2008) 297
337. Simulating the migration and growth patterns of Bacillus subtilis, M. Badoual, P. Derbez, M. Aubert, and B. Grammaticos, Physica A 388 (2009) 549
338. Quantum Painleve equations: from continuous to discrete and back, H. Nagoya, B. Grammaticos, A. Ramani, Reg. Chao. Dyn. 13 (2008) 417
339. Contiguity relations for discrete and ultradiscrete Painleve equations, A. Ramani, B. Grammaticos, R. Willox, J. Nonlin. Math. Phys. 15 (2008) 353
340. Modelling tumour cell migration: from microscopic to macroscopic, C. Deroulers, M. Aubert, M. Badoual, B. Grammaticos, Phys. Rev. E 79 (2009) 031917
341. Investigating the integrability of the Lyness mapping, B. Grammaticos, A. Ramani, T. Tamizhmani, J. Phys. A 42 (2009) 454009
342. Painleve equations: continuous, discrete and ultradiscrete, B. Grammaticos, A. Ramani, in Symmetries and Integrability fo Difference Equations, D. Levi, P. Olver, Z. Thomova, P. Winternitz editors, Cambridge Univ. Press, 2011, p.50
343. Folding transformations for quantum Painleve equations, A. Ramani, H. Nagoya, B. Grammaticos, T. Tamizhmani, J. Phys. A 42 (2009) 095211

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344. The number of Painleve equations is infinite, A. Ramani, B. Grammaticos, Phys. Lett. A 373 (2009) 3028
345. A discrete-time model for cryptic oscillations in predator-prey systems, R. Willox, A. Ramani, B. Grammaticos, Physica D 22 (2009) 2238
346. On two (not so) new integrable partial difference equations, A. Ramani, B. Grammaticos, R. Willox, J. Satsuma, J. Phys. A 42 (2009) FT 282002
347. Scoring the athletic performance for age groups, B. Grammaticos, New Stud. Athl. 24 (2009) 63
348. How to detect the integrability of discrete systems, B. Grammaticos, R.G. Halburd, A. Ramani, C.M. VIallet, J. Phys. A 45 (2009) 454002
349. Deautonomising integrable non-QRT mappings, A.S. Carstea, A. Ramani, B. Grammaticos, J. Phys. A 42 (2009) 485207
350. On the non-autonomous form of the Q4 mapping and its relation to elliptic Painleve equations, A. Ramani, B. Grammaticos, A.S. Carstea, J. Phys. A 42 (2009) FT 322003
351. Singularity confinement property for the (non-autonomous) Adler-Bobenko-Suris integrable lattice equations, B. Grammaticos, A. Ramani, Lett. Math. Phys. 92 (2010) 33. cnrs09
352. Modelling the morphology of migrating bacterial colonies, A. Nishiyama, T. Tokihiro, M. Badoual, B. Grammaticos, Physica D 239 (2010) 1573.

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353. Modelling intercellular communication and its effects on tumour invasion, M. Badoual, C. Deroulers, M. Aubert, B. Grammaticos, Phys. Biol. 7 (2010) 046013
354. Second-degree discrete Painlevé equations conceal first-degree ones, A. Ramani, B. Grammaticos, N. Joshi, J. Phys. A 43 (2010) 175207
355. Folding transformations and HKY mappings, B. Grammaticos, A. Ramani, R. Willox, J. Nonlin. Math. Phys. 18 (2011) 75.
356. How to discretise differential systems in a systematic way, M. Murata, J. Satsuma, A. Ramani, B. Grammaticos, J. Phys. A 43 (2010) 315203.
357. Generalised QRT mappings with periodic coefficients, A. Ramani, B. Grammaticos, R. Willox, Nonlinearity 24 (2011) 113.
358. Mappings of Hirota-Kimura-Yahagi type can have periodic coefficients, too, B. Grammaticos, A. Ramani, K.M. Tamizhmani, J. Phys. A 44 (2011) 015206.
359. From discrete Painlevé equations to mappings with periodic coefficients and back, A. Ramani, B. Grammaticos, K.M. Tamizhmani, J. Phys. A 43 (2010) 485202
360. Discretising systematically the Painlevé equations, M. Murata, J. Satsuma, A. Ramani, B. Grammaticos, Physica D 240 (2011) 305
361. Solving the ultradiscrete KdV equation, R. Willox, Y. Nakata, J. Satsuma, A. Ramani, B. Grammaticos, J. Phys A FT 43 (2010) 482003
362. Modelling the role of water in Bacillus subtilis colonies, X. Mezanges, M. Badoual, C. Regeard, C. Deroulers, C. Gerin, B. Grammaticos, Phys. Rev. E 85 (2012) 041913
363. On two integrable lattice equations and their interpretation, C. Scimiterna, A. Ramani, B. Grammaticos, J. Phys. A FT 44 (2011) 032002

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365. Dynamical Studies of Equations from the Gambier Family, P. Guha, A. Ghose Choudhury, B. Grammaticos, Sigma 7 (2011) 28
367. Miura transformations and the various guises of integrable lattice equations, B. Grammaticos, A. Ramani, C. Scimiterna, R. Willox, J. Phys. A FT 44 (2011) 152004
368. Stochastic and deterministic simulations of a genetic oscillation model with time-delay and reductions, S. Bottani, B. Grammaticos, Chaos, Solitons & Fractals 45 (2012) 588
369. Improving the time-machine: estimating the date of birth of grade II gliomas, C. Gerin, J. Pallud, B. Grammaticos, E. Mandonnet, C. Deroulers, P. Varlet, L. Capelle, L. Taillandier, L. Bauchet, H. Duffau, M. Badoual, Cell Prolif. 45 (2012) 76
370. A KdV cellular automaton without integers, R. Willox, J. Satsuma, A. Ramani, B. Grammaticos, Contemporry Mathematics 580 (2012) 135
371. Linearisable QRT mappings, A. Ramani, B. Grammaticos, J. Satsuma, N. Mimura, J. Phys. A 44 (2011) 425201
372. Discretising the Painlevé equations à la Hirota-Mickens, B. Grammaticos, A. Ramani, J. Satsuma, R. Willox, J. Math. Phys. 53 (2012) 023506

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373. A new family of discrete Painlevé equations and associated linearisable systems, A. Ramani, B. Grammaticos, J. Nonlin. Math. Phys. 20 (2013) 153
374. On the explicit integration of a class of linearisable mappings, A. Ramani, B. Grammaticos, J. Satsuma, J. Phys. A 45 (2012) 365202
375. From Yang-Baxter maps to integrable recurrences, B. Grammaticos, A. Ramani, C.-M. Viallet, J. Nonlin. Math. Phys. 20 (2013) 260.
376. Higher linearisable mappings and their explicit integration, A. Ramani, B. Grammaticos, K.M. Tamizhmani, T. Tamizhmani, J. Phys. A 46 (2013) 065201.
377. Quantitative characterization of the limits of low-grade gliomas, C. Gerin, J. Pallud, C. Deroulers, P. Varlet, C. Oppenheim, F.X. Roux, B. Grammaticos, M. Badoual, Neuro-Oncology 15 (2013) 1379
378. Linearisable ultradiscrete systems with sign variables and the confinement of singularities, N. Mimura, J. Satsuma, A. Ramani, B. Grammaticos, J. Math. Phys. 54 (2013) 023504
379. Shot put with lighter implements, B. Grammaticos, to appear in New Stud. Athl.
380. Ultra-discrete equations and singularity confinement test for integrability, N. Mimura, S. Isojima, M. Murata, J. Satsuma, B. Grammaticos and A. Ramani, Rep. RIAM Symp. No. 22AO-S8 (2011) 23

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381. A sine-Gordon cellular automaton and its exotic solitons, B. Grammaticos, A. Ramani, R. Willox, J. Phys. A 46 (2013) 145204.
382. Discrete Painlevé equations: an integrability paradigm, B. Grammaticos, A. Ramani, Phys. Scr. 89 (2014) 038002.
383. Contiguity relations for linearisable systems of Gambier type, A. Ramani, B. Grammaticos. P Guha, J. Nonlin. Math. Phys. 20 (2013) 565
384. An edema-based model for diffuse low-grade gliomas: application to clinical cases under radiotherapy, M. Badoual, C. Gerin, C. Deroulers, B. Grammaticos, J-F. Llitjos, J. Pallud, Cell Prolif. 47 (2014) 369.
385. Second degree Painlevé equations and their contiguity relations, B. Grammaticos, A. Ramani, P. Guha, Reg. Chao. Dyn. 19 (2014) 37.
386. The ultradiscrete sine-Gordon equation: introducing the oiston, R. WIllox, A. Ramani, B. Grammaticos, Proceedings of RIAM 2013, Kyushu, 25AO-S2 (2014) 29.
387. Solutions of the lattice sine-Gordon equation and the solitons of its cellular automaton, R. WIllox, A. Ramani, B. Grammaticos, J. Phys. A 47 (2014) 125202.
388. Senkeika kanoshazo no shokichikukan (the space of initial conditions for linearizable mappings) in japanese, T. Takenawa, M. Eguchi, B. Grammaticos, Y. Ohta, A. Ramani, J. Satsuma, RIMS Kokyuroku 1302 (2003) 137

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389. Strongly asymmetric discrete Painlevé equations: the additive case, B. Grammaticos, A. Ramani, K.M. Tamizhmani, T. Tamizhmani, J. Satsuma, J. Math. Phys. 55 (2014) 053503.
390. On two discrete Painlevé equations with high periodicities, A. Ramani, B. Grammaticos, J. Phys. A FT 47 (2014) 192001.
391. On the integrability of a new lattice equation, B. Grammaticos, A. Ramani, C. Scimiterna, J. Satsuma, J. Phys. A 47 (2014) 405201.
392. Comparing the best athletic performances of the two sexes, B. Grammaticos, Y. Charon to appear in New Stud. Athl.
393. Discrete Painlevé equations with maximal periodicities, A. Ramani, B. Grammaticos, J. Phys. A 47 (2014) 385201.
394. Discrete Painlevé equations associated with the affine Weyl group E8, A. Ramani, B. Grammaticos
395. Deautonomisation by singularity confinement: an algebro-geometric justification, T. Mase, R. Willox, B. Grammaticos, A. Ramani
396. The redemption of singularity confinement, A. Ramani, B. Grammaticos, R. Willox, T. Mase, M. Kanki

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