About Linearization of Infinite-Dimensional Hamiltonian Systems

被引：0
作者：
Michela Procesi
Laurent Stolovitch
机构：
[1] Universitá degli Studi Roma Tre,Dipartimento di Matematica e Fisica
[2] L.go Murialdo,CNRS and Laboratoire J.
[3] Université Côte d’Azur,A. Dieudonné U.M.R. 7351
来源：
Communications in Mathematical Physics | 2022年 / 394卷
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摘要：
This article is concerned with analytic Hamiltonian dynamical systems in infinite dimension in a neighborhood of an elliptic fixed point. Given a quadratic Hamiltonian, we consider the set of its analytic higher order perturbations. We first define the subset of elements which are formally symplectically conjugated to a (formal) Birkhoff normal form. We prove that if the quadratic Hamiltonian satisfies a Diophantine-like condition and if such a perturbation is formally symplectically conjugated to the quadratic Hamiltonian, then it is also analytically symplectically conjugated to it. Of course what is an analytic symplectic change of variables depends strongly on the choice of the phase space. Here we work on periodic functions with Gevrey regularity.
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页码：39 / 72
页数：33
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