Georgi Popov

KAM theorem for Gevrey Hamiltonians

We consider Gevrey perturbations

Liouville billiard tables and an inverse spectral result

H

Invariants of Isospectral Deformations and Spectral Rigidity

of a completely integrable Gevrey Hamiltonian

ASYMPTOTICS OF THE NUMBER OF RESONANCES IN THE TRANSMISSION PROBLEM

H_0

Resonances for transparent obstacles

. Given a Cantor set

Distribution of the resonances and local energy decay in the transmission problem

\Omega_\kappa

Resonances Near the Real Axis¶for Transparent Obstacles

defined by a Diophantine condition, we find a family of KAM invariant tori of

Quasimodes with exponentially small errors associated with elliptic periodic rays

H

DISTRIBUTION OF RESONANCES AND LOCAL ENERGY DECAY IN THE TRANSMISSION PROBLEM. II

with frequencies

Discrete analog of the projective equivalence and integrable billiard tables

\omega\in \Omega_\kappa