Stability Islands in the vicinity of separatrices of near-integrable symplectic maps

Discrete and Continuous Dynamical Systems - Series B

Volumn 10, Issue 2-3, 2008, Pages 681-698

  Simó, Carles ^a   Treschev, Dmitri ^b  

^a UNIVERSITY OF BARCELONA   (Spain)

^b STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

Area preserving maps; Lobes defined by invariant manifold; Separatrix maps; Stability islands

Indexed keywords

EID: 73149116812     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2008.10.681     Document Type: Article

References (10)

1. S. A. Dovbysh, Splitting of separatrices and generation of isolated periodic solutions in Hamiltonian systems with one and a half degrees of freedom, Uspekhi. Mat. Nauk., 44 (1989), 229-230 (in Russian).
2. E. Fontich and C. Simó, The Splitting of Separatrices for Analytic Diffeomorphisms, Erg. Th. & Dyn. Systems, 10 (1990), 295-318.
3. V. Gelfreich, A proof of the exponentially small transversality of the séparatrices for the standard map, Comm. Math. Phys., (1999), 155-216.
4. V. Gelfreich and V. Lazutkin, Splitting of separatrices: perturbation theory and exponential smallness, Russian Math. Surveys, 56 (2001), 499-558.
5. V. Gelfreich and C. Simó, High-precision computations of divergent asymptotic series and homoclinic phenomena, This Volume.
6. V. V. Kozlov, Splitting of separatrices and generation of isolated periodic solutions in Hamiltonian systems with one and a half degrees of freedom, Uspekhi. Mat. Nauk., 41 (1986), 177-178 (in Russian).
7. J. Moser, The analytic invariants of an area-preserving mapping near a hyperbolic fixed point, Commun. Pure and Appl. Math., 9 (1956), 673-692.
8. C. Simó, and A. Vieiro, Some relevant aspects of area preserving maps and the planar conservative Hénon map, Preprint (2007), Univ. Barcelona.
9. Ya. G. Sinai, Several exact results on decay of correlations, in the book "Zaslavsky G.M. Statistical Irreversibility in Nonlinear Systems" [Current Problems in Physics] "Nauka", Moscow 1970 (in Russian).
10. D. V. Treschev, Hyperbolic tori and asymptotic surfaces in Hamiltonian systems, Russian J. of Math. Phys., 2 (1994), 93-110.