Exponential Decay of Expansive Constants

TL;DR

This paper investigates how the exponential decay rate of expansive constants in a map relates to the map's topological entropy, establishing bounds involving box dimension.

Contribution

It introduces a novel analysis of the exponential decay of expansive constants and links it to topological entropy and box dimension.

Findings

Decay rate times box dimension bounds topological entropy

Expansiveness is preserved under iteration

Provides new bounds connecting decay rate and entropy

Abstract

A map $f$ on a compact metric space is expansive if and only if $f^n$ is expansive. We study the exponential rate of decay of the expansive constant of $f^n$. A major result is that this rate times box dimension bounds topological entropy.