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arXiv · 2003.13445

A generalized Grobman-Hartman theorem for nonautonomous dynamics

Lucas Backes·Davor Dragičević
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Abstract

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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Lucas Backes, Davor Dragičević. 2021-06-21. A generalized Grobman-Hartman theorem for nonautonomous dynamics. https://doi.org/10.1007/s13348-021-00327-4

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