Measure and Capacity of Wandering Domains in Gevrey Near-integrable Exact Symplectic Systems - Couverture souple

Lazzarini, Laurent; Marco, Jean-Pierre; Sauzin, David

Couverture souple

ISBN 10 : 147043492X ISBN 13 : 9781470434922

Editeur : American Mathematical Society, 2019

Synopsis

A wandering domain for a diffeomorphism $\Psi $ of $\mathbb A^n=T^*\mathbb T^n$ is an open connected set $W$ such that $\Psi ^k(W)\cap W=\emptyset $ for all $k\in \mathbb Z^*$. The authors endow $\mathbb A^n$ with its usual exact symplectic structure. An integrable diffeomorphism, i.e., the time-one map $\Phi ^h$ of a Hamiltonian $h: \mathbb A^n\to \mathbb R$ which depends only on the action variables, has no nonempty wandering domains.

The aim of this paper is to estimate the size (measure and Gromov capacity) of wandering domains in the case of an exact symplectic perturbation of $\Phi ^h$, in the analytic or Gevrey category. Upper estimates are related to Nekhoroshev theory; lower estimates are related to examples of Arnold diffusion. This is a contribution to the ``quantitative Hamiltonian perturbation theory'' initiated in previous works on the optimality of long term stability estimates and diffusion times; the emphasis here is on discrete systems because this is the natural setting to study wandering domains.

A propos du livre

À propos de l'auteur

Laurent Lazzarini, Universite Paris VI, France.

Jean-Pierre Marco, Universite Paris VI, France.

David Sauzin, Observatoire de Paris, France.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2019
• Langue: anglais
• ISBN 10: 147043492X
• ISBN 13: 9781470434922
• Reliure: Broché
• Nombre de pages: 106
• Coordonnées du fabricant: Buchpark GmbH; https://www.buchpark.de; ; Krügerweg 1; Trebbin; Brandenburg; 14959; Allemagne