Each compact orientable surface of positive genus admits an expansive homeomorphism

Thomas O'Brien, William Reddy
1970 Pacific Journal of Mathematics  
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 S 2 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
more » ... tropy and existence of interesting minimal sets.
doi:10.2140/pjm.1970.35.737 fatcat:akw347qu7jg4zl63wnwh6uojme