KAM theorem for Gevrey Hamiltonians

Ergodic Theory and Dynamical Systems

Volumn 24, Issue 5, 2004, Pages 1753-1786

  Popov, G ^a  

^a Universite de Nantes   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 9344247432     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385704000458     Document Type: Article

References (18)

1. J. Bruna. An extension theorem of Whitney type for non quasi-analytic classes of functions. J. London Math. Soc. 22(2) (1980), 495-505.
2. L, Chierchia and G. Gallavotti. Smooth prime integrals for quasi-integrable Hamiltonian systems. Nuovo Cimento B(11) 67(2) (1982), 277-295.
3. A. Giorgilli and A. Morbidelli. Invariant KAM tori and global stability for Hamiltonian systems. Z. Angew. Math. Phys. 48(1) (1997), 102-134.
4. M. Herman. Inégalités 'a priori' pour des tores lagrangiens invariants par des difféomorphismes symplectiques. Publ. Math. Inst. Hautes Études Sci. 70 (1989), 47-101.
5. H. Komatsu. The implicit function theorem for ultradifferentiable mappings. Proc. Japan Acad. A 55 (1979), 69-72.
6. S. Kuksin. Analysis of Hamiltonian PDE's (Oxford Lecture Series in Mathematics and its Applications, 19). Oxford University Press, Oxford, 2000.
7. V. Lazutkin. KAM Theory and Semiclassical Approximations to Eigenfunctions. Springer, Berlin, 1993.
8. J. L. Lions and E. Magenes. Problèmes aux limites non homogènes et applications, Vol. 3 (Travaux et recherches mathématiques, 20). Dunod, Paris, 1970.
9. P. Lochak. Canonical perturbation theory: an approach based on joint approximations. Usp. Mat. Nauk 47(6) (1992), 59-140 (Engl. transl. Russian Math. Surveys 47(6) (1992), 57-133).
10. P. Lochak. Canonical perturbation theory: an approach based on joint approximations. Usp. Mat. Nauk 47(6) (1992), 59-140 (Engl. transl. Russian Math. Surveys 47(6) (1992), 57-133).
11. J.-P. Marco and D. Sauzun. Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems. Publ. Math. Inst. Hautes Études Sci. 96 (2002), 199-275.
12. A. Morbidelli and A. Giorgilli. On a connection between KAM and Nekhoroshev's theorems. Physica D 86(1995), 514-516.
13. J. Pöschel. Integrability of Hamiltonian systems on Cantor tori. Comm. Pure Appl. Math. 35 1982), 653-695.
14. J. Pöschel. A lecture on the classical KAM theorem. Proc. Symp. Pure Math. 69 (2001), 707-732.
15. G. Popov. Invariant tori, effective stability and quasi-modes with exponentially small error terms I. Ann. Henri Poincaré 1 (2000), 223-248.
16. G. Popov. Invariant tori, effective stability and quasi-modes with exponentially small error terms II. Ann. Henri Poincaré 1 (2000), 249-279.
17. L. Rodino. Linear Partial Differential Operators in Gevrey Spaces. World Scientific, Singapore, 1993.
18. E. Zehnder. Generalized implicit function theorems with applications to some small divisor problems I. Comm. Pure Appl. Math. 28 (1975), 91-140.