Reminiscences on science at IHÉS. A problem on homoclinic theory and a brief review
Publications Mathématiques de l'IHÉS, Tome S88 (1998), pp. 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},
     pages = {99--117},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {S88},
     year = {1998},
     mrnumber = {1667903},
     zbl = {01784380},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1998__S88__99_0/}
}
TY  - JOUR
AU  - Gallavotti, Giovanni M.
TI  - Reminiscences on science at IHÉS. A problem on homoclinic theory and a brief review
JO  - Publications Mathématiques de l'IHÉS
PY  - 1998
SP  - 99
EP  - 117
VL  - S88
PB  - Institut des Hautes Études Scientifiques
UR  - http://www.numdam.org/item/PMIHES_1998__S88__99_0/
LA  - en
ID  - PMIHES_1998__S88__99_0
ER  - 
%0 Journal Article
%A Gallavotti, Giovanni M.
%T Reminiscences on science at IHÉS. A problem on homoclinic theory and a brief review
%J Publications Mathématiques de l'IHÉS
%D 1998
%P 99-117
%V S88
%I Institut des Hautes Études Scientifiques
%U http://www.numdam.org/item/PMIHES_1998__S88__99_0/
%G en
%F 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, Tome 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 | Zbl

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

[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 | Zbl

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

[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 | Zbl

[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

[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 | Zbl

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 | Zbl

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