Rescaled expansivity and separating flows

TL;DR

This paper explores the relationship between different notions of expansivity in dynamical systems, establishing conditions under which one form implies another and characterizing expansive flows on compact spaces.

Contribution

It provides sufficient conditions linking Komuro and rescaled expansivity and characterizes Katok-Hasselblatt expansivity via separating flows and fixed point openness.

Findings

Komuro expansivity implies rescaled expansivity under certain conditions.

A flow is Katok-Hasselblatt expansive iff it is separating with an open fixed point set.

Abstract

In this article we give sufficient conditions for Komuro expansivity to imply the rescaled expansivity recently introduced by Wen and Wen. Also, we show that a flow on a compact metric space is expansive in the sense of Katok-Hasselblatt if and only if it is separating in the sense of Gura and the set of fixed points is open.