Positively n-expansive homeomorphisms and the L-shadowing property

TL;DR

This paper investigates the dynamics of positively n-expansive homeomorphisms with the L-shadowing property, establishing that such systems can only exist in finite metric spaces, thus advancing understanding of their structural limitations.

Contribution

It introduces the L-shadowing property for n-expansive homeomorphisms and proves their existence is restricted to finite metric spaces.

Findings

Positively n-expansive homeomorphisms with L-shadowing only exist in finite spaces

The L-shadowing property influences the possible dynamics of n-expansive systems

Finite metric spaces are the only setting for these homeomorphisms

Abstract

We discuss further the dynamics of n-expansive homeomorphisms with the shadowing property, started in [7]. The L-shadowing property is defined and the dynamics of n-expansive homeomorphisms with such property is explored. In particular, we prove that positively n-expansive homeomorphisms with the L-shadowing property can only be defined in finite metric spaces.