A generalized Grobman-Hartman theorem for nonautonomous dynamics
Dynamical Systems
2021-07-14 v3
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 H\"older continuous.
Keywords
Cite
@article{arxiv.2003.13445,
title = {A generalized Grobman-Hartman theorem for nonautonomous dynamics},
author = {Lucas Backes and Davor Dragičević},
journal= {arXiv preprint arXiv:2003.13445},
year = {2021}
}
Comments
V2: Added a missing argument in the proof of the main theorem. V3: Added example and strengthened Theorem 2. Final version