Reminiscences on science at IHÉS. A problem on homoclinic theory and a brief review

Giovanni M. Gallavotti

Publications Mathématiques de l'IHÉS (1998)

  • Volume: S88, page 99-117
  • ISSN: 0073-8301

How to cite


Gallavotti, Giovanni M.. "Reminiscences on science at IHÉS. A problem on homoclinic theory and a brief review." Publications Mathématiques de l'IHÉS S88 (1998): 99-117. <>.

author = {Gallavotti, Giovanni M.},
journal = {Publications Mathématiques de l'IHÉS},
language = {eng},
pages = {99-117},
publisher = {Institut des Hautes Etudes Scientifiques},
title = {Reminiscences on science at IHÉS. A problem on homoclinic theory and a brief review},
url = {},
volume = {S88},
year = {1998},

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
PB - Institut des Hautes Etudes Scientifiques
VL - S88
SP - 99
EP - 117
LA - eng
UR -
ER -


  1. [BCG] G. Benettin , A. Carati, G. Gallavotti, A rigorous implementation of the Jeans-Landau-Teller approximation for adiabatic invariants , Nonlinearity10, 479-507, 1997. Zbl0907.58057MR1438264
  2. [CG] L. Chierchia , G. Gallavotti, Drift and diffusion in phase space , Annales de l'Institut Henri PoincaréB60, 1-144, 1994. Zbl1010.37039MR1259103
  3. [DGJS] S. Delshams , V.G. Gelfreich, A. Jorba, T.M. Seara, Exponentially small splitting of separatrices under fast quasiperiodic forcing, Communications in Mathematical Physics189, 35-72, 1997. Zbl0897.34042MR1478530
  4. [E] L.H. Eliasson , Absolutely convergent series expansions for quasi-periodic motions, Mathematical Physics Electronic Journal , 2, 1996. Zbl0896.34035MR1399458
  5. [Ge] V.G. Gelfreich , A proof of exponentially small transversality of the sepratrices for the standard map, in, #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 . 
  6. [GGM0] G. Gallavotti , G. Gentile, V. Mastropietro, Field theory and KAM tori , p. 1-9, Mathematical Physics Electronic Journal, MPEJ, 1, 1995. ( ) Zbl0849.58038MR1359460
  7. [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,, # 97-472. Zbl0936.37034
  8. [GGM2] G. Gallavotti , G. Gentile, V. Mastropietro, HamiltonJacobi equation, heteroclinic chains and Arnol'd diffusion in three time scales systems, #98-4;, #9801004. 
  9. [GGM3] G. Gallavotti , G. Gentile, V. Mastropietro, Melnikov's approximation dominance . Some examples, #9804043 . 
  10. [GGM4] G. Gallavotti , G. Gentile, V. Mastropietro, Homoclinic splitting, II. A possible counterexample to a claim by Rudnev and Wiggins on PhysicaD, #9804017. 
  11. [HM] P. Holmes , J. Marsden, Melnikov's method and Arnold diffusionforperturbations of integrable systems , Journal of Mathematical Physics, 23, 669-676, 1982.. Zbl0497.70025MR649549
  12. 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. Zbl0685.70017MR986267
  13. [T] W. Thirring , Course in Mathematical Physics, vol. 1, p. 133, Springer , Wien, 1983 . Zbl0491.46057MR681697

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