A formal approximation of the splitting of separatrices in the classical Arnold's example of diffusion with two equal parameters

Nonlinearity

Volumn 14, Issue 6, 2001, Pages 1707-1760

  Simó, Carles ^a   Valls, Clàudia ^a  

^a UNIVERSITY OF BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035511358     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/14/6/316     Document Type: Article

References (19)

1. Arnold V I 1964 Instability of dynamical systems with several degrees of freedom Sov. Math. Dokl. 5 581-5
2. Chierchia L and Gallavotti G 1994 Drift and diffusion in phase space Ann. Inst. H Poincaré. Phys. Théor. 60 1-144
3. Delshams A and Gutiérrez P 2000 Homoclinic orbits to invariant tori in Hamiltonian systems Multiple-Time-Scale Dynamical Systems (IMA Vol. Math. Appl. 122) ed C K R T Jones and A Khibnik (Berlin: Springer) pp 1-28
4. Delshams A and Seara T M 1992 An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum Commun. Math. Phys. 150 433-63
5. Delshams A, Gelfreich V G, Jorba A and Seara T M 1997 Exponentially small splitting of separatrices under fast quasiperiodic forcing Commun. Math. Phys. 189 35-71
6. Fontich E and Simó C 1990 Invariant manifolds for near identity differentiable maps and splitting of separatrices Ergod. Theor. Dynam. Syst. 10 319-46
7. Jorba À 1999 A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems Exp. Math. 8 155-95
8. Lochack P, Marco J P and Sauzin D 1999 On the splitting of invariant manifolds in multidimensional near-integrable Hamiltonian systems Preprint
9. Melnikov V K 1963 On the stability of the center for time periodic perturbations Trans. Moscow Math. Soc. 12 3-56
10. Poincaré H 1892 Les Métodes Nouvelles de la Mécanique Céleste vol 1 (Paris: Gauthier-Villars) Poincaré H 1893 Les Métodes Nouvelles de la Mécanique Céleste vol 2 (Paris: Gauthier-Villars) Poincaré H 1899 Les Métodes Nouvelles de la Mécanique Céleste vol 3 (Paris: Gauthier-Villars)
11. Poincaré H 1892 Les Métodes Nouvelles de la Mécanique Céleste vol 1 (Paris: Gauthier-Villars) Poincaré H 1893 Les Métodes Nouvelles de la Mécanique Céleste vol 2 (Paris: Gauthier-Villars) Poincaré H 1899 Les Métodes Nouvelles de la Mécanique Céleste vol 3 (Paris: Gauthier-Villars)
12. Poincaré H 1892 Les Métodes Nouvelles de la Mécanique Céleste vol 1 (Paris: Gauthier-Villars) Poincaré H 1893 Les Métodes Nouvelles de la Mécanique Céleste vol 2 (Paris: Gauthier-Villars) Poincaré H 1899 Les Métodes Nouvelles de la Mécanique Céleste vol 3 (Paris: Gauthier-Villars)
13. Rudnev M and Wiggins S 1998 Existence of exponentially small separatrix splitting and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems Physica D 114 3-80
14. Sauzin D 2001 A new method for measuring the spltiting of invariant manifolds Ann. Sc. Ecole Normale Super. 34
15. Schmidt W M 1980 Diophantine Approximation (Lecture Notes in Mathematics 785) (Berlin: Springer)
16. Simó C 1994 Averaging under fast quasiperiodic forcing Integrable and Chaotic Behaviour in Hamiltonian Systems ed I Seimenis (New York: Plenum) pp 13-34
17. Simó C 2001 Global dynamics and fast indicators Global Analysis of Dynamical Systems ed H W Broer, B Krauskopf and G Vegter (Bristol: IOP Publishing) pp 373-89
18. Simó C 2001 Numerical indicators of the dynamics. Applications to diffusion, in preparation
19. Simó C and Valls C 2001 Exponentially small splitting of separatrices in the classical Arnold's example of diffusion with two equal parameters, in preparation