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Infinite dimensional holomorphy and applications

Holomorphic functions --- Domains of holomorphy

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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 kin 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^no 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.

Symplectic geometry. --- Symplectic groups. --- Domains of holomorphy.

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Infinite dimensional holomorphy and applications

Holomorphic functions --- Domains of holomorphy --- Holomorphy domains --- Analytic continuation --- Functions of several complex variables --- Functions, Holomorphic

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Functional Analysis, Holomorphy and Approximation Theory

Functional analysis --- Holomorphic functions --- Domains of holomorphy --- Approximation theory --- Holomorphy domains --- Analytic continuation --- Functions of several complex variables --- Functions, Holomorphic