Reminiscences on science at IHÉS. A problem on homoclinic theory and a brief review
Publications Mathématiques de l'IHÉS, Volume S88  (1998), p. 99-117
@article{PMIHES_1998__S88__99_0,
     author = {Gallavotti, Giovanni M.},
     title = {Reminiscences on science at IH\'ES. A problem on homoclinic theory and a brief review},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {S88},
     year = {1998},
     pages = {99-117},
     zbl = {01784380},
     mrnumber = {1667903},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1998__S88__99_0}
}
Gallavotti, Giovanni M. Reminiscences on science at IHÉS. A problem on homoclinic theory and a brief review. Publications Mathématiques de l'IHÉS, Volume S88 (1998) , pp. 99-117. http://www.numdam.org/item/PMIHES_1998__S88__99_0/

[BCG] G. Benettin , A. Carati, G. Gallavotti, A rigorous implementation of the Jeans-Landau-Teller approximation for adiabatic invariants , Nonlinearity 10, 479-507, 1997. | MR 1438264 | Zbl 0907.58057

[CG] L. Chierchia , G. Gallavotti, Drift and diffusion in phase space , Annales de l'Institut Henri Poincaré B 60, 1-144, 1994. | Numdam | MR 1259103 | Zbl 1010.37039

[DGJS] S. Delshams , V.G. Gelfreich, A. Jorba, T.M. Seara, Exponentially small splitting of separatrices under fast quasiperiodic forcing, Communications in Mathematical Physics 189, 35-72, 1997. | MR 1478530 | Zbl 0897.34042

[E] L.H. Eliasson , Absolutely convergent series expansions for quasi-periodic motions, Mathematical Physics Electronic Journal , 2, 1996. | MR 1399458 | Zbl 0896.34035

[Ge] V.G. Gelfreich , A proof of exponentially small transversality of the sepratrices for the standard map, in mp_arc@math.utexas.edu, #98-270: this recent paper, besides clarifyng various aspects of previous papers, provides an accurate exposition of the main ideas (and appropriate references) of the other papers by the russian school .

[GGM0] G. Gallavotti , G. Gentile, V. Mastropietro, Field theory and KAM tori , p. 1-9, Mathematical Physics Electronic Journal, MPEJ, 1, 1995. ( http://mpej.unige.ch ) | MR 1359460 | Zbl 0849.58038

[GGM1] G. Gallavotti , G. Gentile, V. Mastropietro, Separatrix splitting for systems with three time scales, to appear in Communications in Mathematical Physics, preprint in Pendulum: separatrix splitting, mp_arc@math.utexas.edu, # 97-472. | Zbl 0936.37034

[GGM2] G. Gallavotti , G. Gentile, V. Mastropietro, HamiltonJacobi equation, heteroclinic chains and Arnol'd diffusion in three time scales systems, mp_arc@math.utexas.edu #98-4; chao-dyn@xyz.lanl.gov, #9801004.

[GGM3] G. Gallavotti , G. Gentile, V. Mastropietro, Melnikov's approximation dominance . Some examples, chaodyn@xyz.lanl.gov #9804043 .

[GGM4] G. Gallavotti , G. Gentile, V. Mastropietro, Homoclinic splitting, II. A possible counterexample to a claim by Rudnev and Wiggins on Physica D, chao-dyn@xyz.lanl.gov #9804017.

[HM] P. Holmes , J. Marsden, Melnikov's method and Arnold diffusionforperturbations of integrable systems , Journal of Mathematical Physics, 23, 669-676, 1982.. | MR 649549 | Zbl 0497.70025

See also: Holmes, P., Marsden, J., Scheurle, J.: Exponentially Small Splittings of Separatrices with applications to KAM Theory and Degenerate Bifurcations, Contemporary Mathematics , 81, 213-244, 1988. | MR 986267 | Zbl 0685.70017

[T] W. Thirring , Course in Mathematical Physics, vol. 1, p. 133, Springer , Wien, 1983 . | MR 681697