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KAM theorem for Gevrey Hamiltonians
  • G. Popov
  • Mathematics
  • Ergodic Theory and Dynamical Systems
  • 19 May 2003
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 ofExpand
On the Contribution of Degenerate Periodic Trajectories to the Wave-Trace
Abstract:This paper is concerned with the wave trace Z(t)of a selfadjoint elliptic pseudodifferential operator on a compact manifold. It is devoted to the contribution of degenerate periodicExpand
Resonances Near the Real Axis¶for Transparent Obstacles
Abstract:The purpose of this paper is to study the resonances for the transmission problem for a strictly convex obstacle in Rnn≥ 2. If the speed of propagation in the interior of the body isExpand
Quasimodes with exponentially small errors associated with elliptic periodic rays
The aim of this paper is to construct compactly supported Gevrey quasimodes with exponentially small discrep- ancy for the Laplace operator with Dirichlet boundary conditions in a domain X withExpand
Invariants of Isospectral Deformations and Spectral Rigidity
We introduce a notion of weak isospectrality for continuous deformations. Consider the Laplace–Beltrami operator on a compact Riemannian manifold with Robin boundary conditions. Given a KroneckerExpand
The possibility of evidence-based psychiatry: depression as a case
The strengths and weaknesses of research onto the causality of relationship between diagnosis and therapy of major depressive disorder are examined and what could be done to strengthen eventual claims on causality are suggested. Expand
This paper is concerned with the resonances of the transmission problem for a transparent bounded strictly convex obstacle O with a smooth boundary (which may contain an impenetrable body). If theExpand
Distribution of the resonances and local energy decay in the transmission problem
We study the resonances associated to the transmission problem for a strictly convex obstacle provided that the speed of propagation of the waves in the interior of the obstacle is strictly greaterExpand
Invariant Tori, Effective Stability, and Quasimodes with Exponentially Small Error Terms I –¶Birkhoff Normal Forms
Abstract. The aim of this paper (part I and II) is to explore the relationship between the effective (Nekhoroshev) stability for near-integrable Hamiltonian systems and the semi-classical asymptoticsExpand