Georgi Popov
KAM Theorem for Gevrey Hamiltonians
(457K, Postscript)
ABSTRACT. We consider Gevrey perturbations $H$ of a completely integrable
Gevrey Hamiltonian $H_0$. Given a
Cantor set $\Omega_\kappa$ defined by a Diophantine condition,
we find a family
of 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 quasiperiodic motion near
$\Lambda$.