Anomalous cw-expansive surface homeomorphisms

TL;DR

This paper demonstrates that the genus two surface can support a cw-expansive homeomorphism featuring a fixed point with a non-locally connected local stable set, revealing complex dynamical behaviors on surfaces.

Contribution

It introduces the first example of a cw-expansive surface homeomorphism with a fixed point having a non-locally connected stable set.

Findings

Existence of cw-expansive homeomorphism on genus two surface

Presence of a fixed point with non-locally connected stable set

Advancement in understanding surface dynamical systems

Abstract

We prove that the genus two surface admits a cw-expansive homeomorphism with a fixed point whose local stable set is not locally connected.