Phase transitions for suspension flows

TL;DR

This paper investigates the thermodynamic formalism of suspension flows over countable alphabets, focusing on the regularity of the pressure function and conditions leading to phase transitions, including examples with infinitely many such transitions.

Contribution

It provides new conditions for the pressure function's regularity and constructs examples with countably many phase transitions in suspension flows.

Findings

Conditions for pressure to be real analytic or have phase transitions.

Existence of potentials with countably many phase transitions.

Insights into the thermodynamic behavior of suspension flows.

Abstract

This paper is devoted to study thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the pressure function. We establish conditions for the pressure function to be real analytic or to exhibit a phase transition. We also construct an example of a potential for which the pressure has countably many phase transitions.