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 
$\Lambda$.