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OverviewA 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. Full Product DetailsAuthor: Laurent Lazzarini , Jean-Pierre Marco , David SauzinPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.183kg ISBN: 9781470434922ISBN 10: 147043492 Pages: 106 Publication Date: 30 March 2019 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationLaurent Lazzarini, Universite Paris VI, France. Jean-Pierre Marco, Universite Paris VI, France. David Sauzin, Observatoire de Paris, France. Tab Content 6Author Website:Countries AvailableAll regions |