A note on the differentiability of Palmer's topological equivalence for discrete systems
Dynamical Systems
2021-05-03 v1
Abstract
A linear system of difference equations and a nonlinear perturbation are considered. We propose sufficient conditions to ensure that the homeomorphism of topological equivalence between them is actually a diffeomorphism. These conditions consider that the linear part satisfies a dichotomy on the positive half-line, while the perturbation satisfies boundness and Lipschitzness conditions, and anothers that are tailored for our goal. The family of dichotomies that we study consider (but are not limited to) the exponential and nonuniform exponential dichotomies. We discuss the possibility of extending this result to a higher class of differentiability.
Keywords
Cite
@article{arxiv.2104.14592,
title = {A note on the differentiability of Palmer's topological equivalence for discrete systems},
author = {Álvaro Castañeda and Néstor Jara},
journal= {arXiv preprint arXiv:2104.14592},
year = {2021}
}