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KAM theorem for Gevrey Hamiltonians

Published online by Cambridge University Press:  18 October 2004

G. POPOV
G. POPOV
Affiliation:
Université de Nantes, Département de Mathématiques, UMR 6629 du CNRS, 2, rue de la Houssinière, BP 92208, 44072 Nantes Cedex 03, France (e-mail: [email protected])
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Abstract

We consider Gevrey perturbations H of a completely integrable non-degenerate Gevrey Hamiltonian H0. Given a Cantor set $\Omega_\kappa$ defined by a Diophantine condition, we find a family of Kolmogorov–Arnold–Moser (KAM) invariant tori of H with frequencies $\omega\in \Omega_\kappa$ which is Gevrey smooth in a Whitney sense. Moreover, we obtain a symplectic Gevrey normal form of the Hamiltonian in a neighborhood of the union $\Lambda$ of the invariant tori. This leads to effective stability of the quasi-periodic motion near $\Lambda$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 5 , October 2004 , pp. 1753 - 1786
Copyright
© 2004 Cambridge University Press

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