Recent results on the separatrix splitting for the standard map
Séminaire de théorie spectrale et géométrie, Tome 11 (1992-1993), pp. 157-165 
@article{TSG_1992-1993__11__157_0,
     author = {V. F. Lazutkin},
     title = {Recent results on the separatrix splitting for the standard map},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {157--165},
     year = {1992-1993},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {11},
     doi = {10.5802/tsg.138},
     zbl = {0921.58046},
     mrnumber = {1715950},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.138/}
}
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V. F. Lazutkin. Recent results on the separatrix splitting for the standard map. Séminaire de théorie spectrale et géométrie, Tome 11 (1992-1993), pp. 157-165. doi: 10.5802/tsg.138

[C] B. V. Chirikov, A universal instability of many-dimensional oscillator systems, Physics Reports 52 ( 1979), 263-279. | MR

[CNP] B. Candelperger, J.-C. Nosmas, F. Pham, Premiers pas en calcul étranger, Ann. Inst. Fourier, Grenoble 43 , no. l ( 1993), 201-224. | Numdam | MR | Zbl

[FS] E. Fontich, C. Simó, The splitting of separatrices for analytic diffeomorphisms, Ergod. Th. Dynam. Sys. 10 ( 1990), 295-318. | MR | Zbl

[GLS] V. G. Gelfreich, V.F. Lazutkin, N. V. Svanidze, A refined formula for the separatrix splitting for the standard map, Physica D (to appear). | MR | Zbl

[GLST] V. G. Gelfreich , V.F. Lazutkin, C. Simó, M.B. Tabanov, Fern-like structures in the wild set of the standard and semistandard maps in C2, International Journal of Bifurcation and Chaos 2, no.2 ( 1992), 353-370. | MR | Zbl

[GLT] V. G. Gelfreich, V. F. Lazutkin , M. B. Tabanov, Exponentially small splitting in hamiltonian systems, Chaos 1, no.2 ( 1991), 137-142. | MR | Zbl

[G] J. M. Greene, A method for determining a stochastic transition, J. Math. Phys. 20 ( 1979), 1183-1201.

[GP] J. M. Greene, I. C. Percival, Hamiltonian maps in the complex plane, Physica D 3 ( 1981), 530-548. | MR

[HMS] P. Holmes, J. Marsden, J. Scheurle, Exponentially Small Splitting of Separatrices with Applications to KAM Theory and degenerate Bifurcations, Contemporary Mathematics 81 ( 1988), 213-244. | MR | Zbl

[Ll] V. F. Lazutkin, Splitting of separatrices for the Chirikov's standard map., Preprint ( 1984), VINITI 6372/84. | MR | Zbl

[L2] V. F. Lazutkin, Exponential splitting of separatrices and an analytical integral for the semistandard map, Preprint no.7, Université Paris VII ( 1991), 53 p.

[L3] V. F. Lazutkin, Resurgent approach to the separatrices splitting, EQUADIFF 91, Iternational Conference on Differential Equations, Barcelona, Spain, 26-31 August 1991, vol.1 (C.Perelló, C.Simó, J. Solà-Morales, eds.), World Scientific, Singapore-New Jersey-London-Hong Kong, 1993, pp. 163-176. | MR | Zbl

[LS] V. F. Lazutkin, C. Simó, Separatrix splitting for the standard map via resurgence, in preparation.

[LST] V. F. Lazutkin , I. G. Schachmanski M. B., Tabanov, Splitting of separatrices for standard and semistandard mappings, Physica D 40 ( 1989), 235-248. | MR | Zbl

[N] A.I. Neishtadt, On the accuracy of the perturbation theory for systems with one rapid variable, Prikladnaya Matematika i Mekhanika 45 ( 1981), 80-87. (Russian) | Zbl

[Pe] I. C. Percival, Chaotic boundary of a Hamiltonian map, Physica D 6 ( 1982), 67-77. | MR

[Po] H. Poincaré, , Les Méthodes Nouvelles de la Méchanique Céleste,Vols 1-3, Gauthier-Villars, Paris, 1892, reprinted by Dover, New York ( 1957). | JFM | Zbl

[Si] C. Simó, private communication.

[Su] Yu. B. Suris, private communication.

[R] J. Riordan, An introduction to combinatorial analysis, Princeton University Press, Princeton, Guilford, 1980. | MR | Zbl

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