About linearization of infinite-dimensional Hamiltonian systems

Autor:	Procesi, Michela, Stolovitch, Laurent
Rok vydání:	2021
Předmět:	Mathematics - Dynamical Systems Mathematics - Functional Analysis 37G05 37K55
Druh dokumentu:	Working Paper
DOI:	10.1007/s00220-022-04398-7
Popis:	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 conjugacted 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. Comment: 28 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2108.00060 Zobrazit plný text záznamu View this record from Arxiv