Strongly isomorphic symbolic extensions for expansive topological flows

TL;DR

This paper proves that expansive topological flows without fixed points and with countably many periodic orbits have a symbolic flow extension, confirming a long-standing question and extending previous smoothness assumptions.

Contribution

It establishes the existence of strongly isomorphic symbolic extensions for a broad class of expansive flows, removing the need for smoothness conditions.

Findings

Flows have the small flow boundary property.

Expansive flows admit symbolic flow extensions.

Answers a question by Bowen and Walters from 1972.

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, i.e. 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.