Strongly Isomorphic Symbolic Extensions for Expansive Topological Flows

Abstract

Abstract In this paper, we prove that finite-dimensional topological flows without fixed points and having a countable number of periodic orbits, have the small flow boundary property. This enables us to answer positively a question of Bowen and Walters from 1972: Any expansive topological flow has a strongly isomorphic symbolic flow extension, that is, an extension by a suspension flow over a subshift. Previously Burguet had shown this is true if the flow is assumed to be $C^{2}$-smooth.