标题： 关于无限维哈密顿系统的线性化 显示英文标题

标题： About linearization of infinite-dimensional Hamiltonian systems

摘要： 本文涉及无限维邻近椭圆不动点的解析哈密顿动力系统。 给定一个二次哈密顿量，我们考虑其解析高阶扰动的集合。 我们首先定义与（形式）Birkhoff标准型形式辛共轭的元素子集。 我们证明，如果二次哈密顿量满足类似狄利克雷条件，并且该扰动形式上与二次哈密顿量辛共轭，则它也与之解析辛共轭。 当然，解析辛变量变换取决于相空间的选择。 在这里，我们研究具有Gevrey正则性的周期函数。 显示英文摘要

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 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.