Each compact orientable surface of positive genus admits an expansive homeomorphism

Thomas V. O’Brien and William Lawrence Reddy

Vol. 35 (1970), No. 3, 737–741

DOI: 10.2140/pjm.1970.35.737

Abstract

It is known that the torus and the orientable surface of genus 2 admit expansive homeomorphisms. In this paper it is shown that all compact orientable surfaces of positive genus admit such homeomorphisms. It remains unknown whether S² admits such a map. By taking products expansive homeomorphisms on higher dimensional manifolds are exhibited. Finally dynamical properties of these examples are discussed. Among these are occurrence and nature of periodic points, topological entropy and existence of interesting minimal sets.

Mathematical Subject Classification

Primary: 54.82

Secondary: 28.00

Milestones

Received: 20 March 1970

Published: 1 December 1970