Exponential estimates of symplectic slow manifolds
Exponential estimates of symplectic slow manifolds
复制标题
辛慢流形的指数估计
DOI：
10.1016/j.jde.2016.03.003
复制
发表时间：
2012
影响因子：
2.4
通讯作者：
C. Wulff
中科院分区：
文献类型：
--
作者：
K. U. Kristiansen;C. Wulff
本文证明了具有2个慢自由度的解析Hamilton慢-快系统的几乎不变辛慢流形的存在性，且其误差场是指数小的.我们允许无限多的快速自由度。我们使用的方法是由麦凯从2004年的论文的动机。该方法不会注意到共振，因此我们不会对垂直于慢流形的运动施加任何限制，除了它是快速和解析的。我们还提出了一个稳定性的结果，并获得了一个推广的结果Gelfreich和Lerman的一个不变的慢流形上的（N）多个快速的自由度。
In this paper we prove the existence of an almost invariant symplectic slow manifold for analytic Hamiltonian slow-fast systems with finitely many slow degrees of freedom for which the error field is exponentially small. We allow for infinitely many fast degrees of freedom. The method we use is motivated by a paper of MacKay from 2004. The method does not notice resonances, and therefore we do not pose any restrictions on the motion normal to the slow manifold other than it being fast and analytic. We also present a stability result and obtain a generalization of a result of Gelfreich and Lerman on an invariant slow manifold to (finitely) many fast degrees of freedom.