Topologically mixing suspension flows over shift spaces

TL;DR

This paper characterizes when suspension flows over shift spaces are topologically mixing, compares these conditions to smooth settings, and shows non-mixing roof functions are densely present.

Contribution

It provides necessary and sufficient conditions for topological mixing in suspension flows over shift spaces and explores the density of non-mixing roof functions.

Findings

Conditions for topological mixing are established.

Non-mixing roof functions form a dense subset.

Differences and similarities with smooth manifold settings are analyzed.

Abstract

We establish necessary and sufficient conditions for suspension flows over certain families of shift spaces to be topologically mixing. We also show the similarities and differences between this case and the smooth measure theoretic setting on a manifold. Additionally, we show that the set of roof functions defined on a shift space that produce suspension flows that are not topologically mixing is dense in the set of all continuous roof functions.