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Splitting of separatrices for the Chirikov standard map. (English. Russian original) Zbl 1120.37039

J. Math. Sci., New York 128, No. 2, 2687-2705 (2005); translation from Zap. Nauchn. Semin. POMI 300, 25-55 (2003).
Summary: This paper is an English translation (made by V. Gelfreich) of V. F. Lazutkin’s work that was published in 1984 by VINITI and thus was not easily available for readers. In the paper, a formula for an exponentially small angle of separatrix splitting of the Chirikov standard map was obtained for the first time. Bibliography: 16 titles and 17 titles added by the translator.

MSC:

37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
37J10 Symplectic mappings, fixed points (dynamical systems) (MSC2010)
54H20 Topological dynamics (MSC2010)
70H09 Perturbation theories for problems in Hamiltonian and Lagrangian mechanics
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References:

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