Borel Isomorphism of SPR Markov Shifts

TL;DR

This paper demonstrates that strongly positively recurrent Markov shifts, including shifts of finite type, can be classified up to Borel conjugacy using their entropy, period, and periodic point counts.

Contribution

It establishes a classification framework for strongly positively recurrent Markov shifts based on key invariants, extending understanding of their Borel conjugacy.

Findings

Classification of strongly positively recurrent Markov shifts by entropy, period, and periodic points.

Inclusion of shifts of finite type within the classification scheme.

Provides a complete invariant set for Borel conjugacy in this class.

Abstract

We show that strongly positively recurrent Markov shifts (in particular shifts of finite type) are classified up to Borel conjugacy by their entropy, period and their numbers of periodic points.