Topological simplification of nonautonomous difference equations

Abstract

In this paper, we continue the study of geometric properties of nonautonomous difference equations in arbitrary Banach spaces which was begun in [2,3]. Building on previous results on invariant fiber bundles and foliations, this paper addresses the problem of topological simplifications via continuous conjugacies and semiconjugacies. In particular, we establish a reduction principle for not necessarily invertible difference equations, as well as a generalized Hartman–Grobman theorem for systems with not necessarily invertible linear part.