Recent results on the separatrix splitting for the standard map

V. F. Lazutkin

Séminaire de théorie spectrale et géométrie (1992-1993)

  • Volume: 11, page 157-165
  • ISSN: 1624-5458

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Lazutkin, V. F.. "Recent results on the separatrix splitting for the standard map." Séminaire de théorie spectrale et géométrie 11 (1992-1993): 157-165. <http://eudml.org/doc/114357>.

@article{Lazutkin1992-1993,
author = {Lazutkin, V. F.},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {selfmap of 2-torus; regular; chaotic; Hamiltonian systems; two degrees of freedom; separatrix splitting; hyperbolic fixed points},
language = {eng},
pages = {157-165},
publisher = {Institut Fourier},
title = {Recent results on the separatrix splitting for the standard map},
url = {http://eudml.org/doc/114357},
volume = {11},
year = {1992-1993},
}

TY - JOUR
AU - Lazutkin, V. F.
TI - Recent results on the separatrix splitting for the standard map
JO - Séminaire de théorie spectrale et géométrie
PY - 1992-1993
PB - Institut Fourier
VL - 11
SP - 157
EP - 165
LA - eng
KW - selfmap of 2-torus; regular; chaotic; Hamiltonian systems; two degrees of freedom; separatrix splitting; hyperbolic fixed points
UR - http://eudml.org/doc/114357
ER -

References

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  3. [FS] E. FONTICH, C. SIMÓ, The splitting of separatrices for analytic diffeomorphisms, Ergod. Th. Dynam. Sys. 10 ( 1990), 295-318. Zbl0706.58061MR1062760
  4. [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). Zbl0812.70017MR1264110
  5. [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. Zbl0874.58028MR1176642
  6. [GLT] V. G. GELFREICH, V. F. LAZUTKIN , M. B. TABANOV, Exponentially small splitting in hamiltonian systems, Chaos 1, no.2 ( 1991), 137-142. Zbl0899.58016MR1135901
  7. [G] J. M. GREENE, A method for determining a stochastic transition, J. Math. Phys. 20 ( 1979), 1183-1201. 
  8. [GP] J. M. GREENE, I. C. PERCIVAL, Hamiltonian maps in the complex plane, Physica D 3 ( 1981), 530-548. Zbl1194.37071MR631185
  9. [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. Zbl0685.70017MR986267
  10. [Ll] V. F. LAZUTKIN, Splitting of separatrices for the Chirikov's standard map., Preprint ( 1984), VINITI 6372/84. Zbl1120.37039MR1993024
  11. [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. 
  12. [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. Zbl0938.37524MR1242238
  13. [LS] V. F. LAZUTKIN, C. SIMÓ, Separatrix splitting for the standard map via resurgence, in preparation. 
  14. [LST] V. F. LAZUTKIN , I. G. SCHACHMANSKI M. B., TABANOV, Splitting of separatrices for standard and semistandard mappings, Physica D 40 ( 1989), 235-248. Zbl0825.58033MR1029465
  15. [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) Zbl0488.70016
  16. [Pe] I. C. PERCIVAL, Chaotic boundary of a Hamiltonian map, Physica D 6 ( 1982), 67-77. Zbl1194.37061MR680895
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  18. [Si] C. SIMÓ, private communication. 
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  20. [R] J. RIORDAN, An introduction to combinatorial analysis, Princeton University Press, Princeton, Guilford, 1980. Zbl0436.05001MR580155

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