Wandering domains and random walks in Gevrey near-integrable systems

Ergodic Theory and Dynamical Systems

Volumn 24, Issue 5, 2004, Pages 1619-1666

  Marco, Jean Pierre ^a   Sauzin, David ^b  

^a SORBONNE UNIVERSITÉ   (France)

^b Institut de Mecanique Celeste et de Calcul des ephemerides   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 9344256664     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385703000786     Document Type: Article

References (16)

1. [Do88] R. Douady. Stabilité ou instabilité des points fixes elliptiques. Ann. Sci. École Norm. Sup. 21 (1988), 1-46.
2. [FM01] E. Fontich and P. Martín. Arnold diffusion in perturbations of analytic integrable Hamiltonian systems. Discr. Continuous Dynam. Sys. 7(1) (2001), 61-84.
3. [He99] M. Herman. Notes de travail. December 1999, unpublished manuscript.
4. [Io79] G. Iooss. Bifurcation of Maps and Applications. North-Holland, Amsterdam, 1979.
5. [LMS03] P. Lochak, J.-P. Marco and D. Sauzin. On the splitting of invariant manifolds in multi-dimensional near-integrable Hamiltonian systems. Mem. Amer. Math. Soc. 163(775) (2003).
6. [LN92] P. Lochak and A.I. Neishtadt. Estimates in the theorem of N. N. Nekhorocheff for systems with a quasi-convex Hamiltonian. Chaos 2 (1992), 495-499.
7. [MS02] J.-P. Marco and D. Sauzin. Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems. Publ. Math. Inst. Hautes Études Sci. 96 (2002), 199-275.
8. [Mei92] J. Meiss. Symplectic maps, variational principles and transport. Rev. Mod. Phys. 64(3) (1992), 795-848.
9. [Moe02] R. Moeckel. Generic drift on Cantor sets of annuli. Celestial Mechanics, Dedicated to Donald Saari for his 60th Birthday (Proc. Int. Conf. on Celestial Mechanics, 15-19 December 1999, Northwestern University, Evanston) (Contemporary Mathematics, 292). Eds. A. Chenciner, R. Cushman, C. Robinson and Z. J. Xia. American Mathematical Society, Providence, RI, 2002, pp. 163-171.
10. [Mos62] J. Moser. On invariant curves of area-preserving mappings of an annulus. Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II (1962), 1-20.
11. [Mos73] J. Moser. Stable and Random Motions in Dynamical Systems. Princeton University Press, Princeton, NJ, 1973.
12. [Ne77] N. N. Nekhoroshev. An exponential estimate of the time of stability of nearly integrable Hamiltonian systems. Usp. Mat. Nauk. 32 (1977), 5-66; Russian Math. Surveys 32 (1977), 1-65.
13. [Ne77] N. N. Nekhoroshev. An exponential estimate of the time of stability of nearly integrable Hamiltonian systems. Usp. Mat. Nauk. 32 (1977), 5-66; Russian Math. Surveys 32 (1977), 1-65.
14. [Pö93] J. Pöschel. Nekhoroshev estimates for quasi-convex Hamiltonian systems. Math. Z. 213 (1993), 187-216.
15. [Sa03] D. Sauzin. Nekhoroshev estimates and instability for Gevrey class Hamiltonians. Dynamical Systems, Part I: Hamiltonian Systems and Celestial Mechanics (Proceedings, Pisa, 2002). Scuola Normale Superiore, Pubblicazioni della classe di scienze (Centro di ricerca matematica 'Ennio De Giorgi': Proceedings), Pisa, 2003, pp. 199-217.
16. [SM71] C. L. Siegel and J. Moser. Lectures on Celestial Mechanics (Grundlehren Math. Wiss., 187). Springer, New York, Heidelberg, 1971.