Partially Expansive Homeomorphisms

TL;DR

This paper explores various forms of expansivity in topological dynamics, introduces new definitions related to topological dimension, and studies the topology of stable sets in surface and three-manifold homeomorphisms.

Contribution

It introduces two new definitions of expansivity linked to topological dimension and analyzes the topology of stable sets under cw-expansive and expansive homeomorphisms.

Findings

Topology of local stable sets studied for surface homeomorphisms

Analysis of expansive homeomorphisms in three-manifolds

Discussion on $C^r$-stable expansivity

Abstract

In this article we consider several forms of expansivity. We introduce two new definitions related with topological dimension. We study the topology of local stable sets under cw-expansive surface homeomorphisms and expansive homeomorphisms of three-manifolds. The problem of $C^r$-stable expansivity is also considered.