非自治动力学的广义Grobman-Hartman定理
A generalized Grobman-Hartman theorem for nonautonomous dynamics
摘要：
本文的目的是推广Bernardes Jr.和Messaoudi从自治到非自治的动力学。更确切地说，我们证明了任何足够小的扰动的非自治线性动力学，承认一个广义指数二分法拓扑共轭的线性部分。此外，我们还证明了在一定的温和的附加条件下，共轭性实际上是Hölder连续的.
英文摘要：
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.
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