Stable/unstable continua of cw-expansive flows

TL;DR

This paper introduces new definitions of local stable and unstable sets for cw-expansive flows without fixed points, and proves the existence of continua with uniform diameter within these sets on Peano continua.

Contribution

It presents novel definitions of local stable/unstable sets and establishes the existence of continua with uniform diameter in cw-expansive flows on Peano continua.

Findings

Existence of continua with uniform diameter in local stable/unstable sets

Introduction of kinematic, geometric, and sectionally geometric definitions

Relations between different types of local stable/unstable sets

Abstract

We introduce distinct definitions of local stable/unstable sets for flows without fixed points, namely, kinematic, geometric, and sectionally geometric, and discuss relations between them. We prove the existence of continua with a uniform diameter within each sectionally geometric local stable/unstable set for cw-expansive flows defined on Peano continua.