论文标题
广义的Grobman-Hartman定理非自主动力学
A generalized Grobman-Hartman theorem for nonautonomous dynamics
论文作者
论文摘要
本说明的目的是将Jr.和Messaoudi建立的Grobman-Hartman定理的最新广义版本从自治动力学到非自主动力学。更确切地说，我们证明，非自主线性动力学的任何足够小的扰动，该动力学接受通用的指数二分法在拓扑结合其线性部分。此外，我们证明在某些轻微的额外条件下，结合实际上是霍尔德连续的。
The purpose of this note is to extend the recent generalized version of the Grobman-Hartman theorem established by Bernardes Jr. and Messaoudi from an autonomous to the nonautonomous dynamics. More precisely, we prove that any sufficiently small perturbation of a nonautonomous linear dynamics that admits a generalized exponential dichotomy is topologically conjugated to its linear part. In addition, we prove that under certain mild additional conditions, the conjugacy is in fact Hölder continuous.
