A topological equivalence result for a family of nonlinear difference systems having generalized exponential dichotomy

TL;DR

This paper establishes conditions under which two nonlinear difference systems with linear parts exhibiting generalized exponential dichotomy are topologically equivalent, including strong and Hölder equivalences when exponential dichotomy holds.

Contribution

It provides new sufficient conditions for topological equivalence of perturbed difference systems with generalized exponential dichotomy, extending existing results.

Findings

Conditions for topological equivalence are derived.

Strong and Hölder equivalences are established under exponential dichotomy.

Results apply to a broad class of nonlinear difference systems.

Abstract

We obtain sufficient conditions ensuring the topological equivalence of two perturbed difference linear systems whose linear part has a property of generalized exponential dichotomy. When the exponential dichotomy is verified, we obtain a strongly and H\"older topological equivalence.