KAM theorem for Gevrey Hamiltonians
Identifieur interne : 000254 ( France/Analysis ); précédent : 000253; suivant : 000255KAM theorem for Gevrey Hamiltonians
Auteurs : G. Popov [France]Source :
- Ergodic Theory and Dynamical Systems [ 0143-3857 ] ; 2004-10.
Abstract
We consider Gevrey perturbations H of a completely integrable non-degenerate Gevrey Hamiltonian H 0. 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 $\Lambda$.
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DOI: 10.1017/S0143385704000458
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