Time change for flows and thermodynamic formalism

TL;DR

This paper investigates how thermodynamic formalism quantities change under time modifications of suspension flows over countable Markov shifts, revealing that such quantities are generally not preserved and providing a topological classification of these flows.

Contribution

It introduces a detailed analysis of the variation of thermodynamic quantities under time changes and offers a topological description of the space of suspension flows based on these quantities.

Findings

No thermodynamic quantity is generally preserved under time change.

The set of suspension flows with finite entropy over the full shift is topologically open.

Develops analytic tools for constructing examples with specific thermodynamic behaviors.

Abstract

This paper is devoted to study how do thermodynamic formalism quantities varies for time changes of suspension flows defined over countable Markov shifts. We prove that in general no quantity is preserved. We also make a topological description of the space of suspension flows according to certain thermodynamic quantities. For example, we show that the set of suspension flows defined over the full shift on a countable alphabet having finite entropy is open. Of independent interest might be a set of analytic tools we use to construct examples with prescribed thermodynamic behaviour.