Expansiveness for flows on noncompact spaces

Abstract

We introduce the concept of topological expansive flow. We prove that this concept is invariant by topological conjugacy and reduces to expansivity in the compact case. We characterize tiopological expansive flows as rescaling expansive flows for which the singularities are isolated points of the space. Finally, we prove that the growth rate of the periodic orbits of a topological expansive flow which is dynamically isolated at infinity is controlled by an entropy-like invariant. This extends Bowen-Walters inequality for expansive flows on compact spaces.