Thermodynamic formalism for some systems with countable Markov structures

TL;DR

This paper investigates the ergodic properties of specific two-dimensional systems with countable Markov partitions, employing thermodynamic formalism to demonstrate exponential decay of correlations.

Contribution

It introduces a thermodynamic formalism approach to analyze ergodic properties of systems with countable Markov structures, establishing exponential decay of correlations.

Findings

Proves exponential decay of correlations in the studied systems

Constructs countable Markov partitions for piecewise smooth systems

Applies thermodynamic formalism to ergodic analysis

Abstract

We study ergodic properties of certain piecewise smooth two-dimensional systems by constructing countable Markov partitions. Using thermodynamic formalism we prove exponential decay of correleations.