Constant slope maps and the Vere-Jones classification

TL;DR

This paper investigates conditions under which certain interval maps are conjugate to constant slope maps, using Vere-Jones classification to analyze the Markov case and relate to topological entropy.

Contribution

It introduces a framework connecting constant slope conjugacy of interval maps with Vere-Jones classification of infinite matrices, focusing on the Markov case.

Findings

Established criteria for conjugacy to constant slope maps.

Linked topological entropy with Vere-Jones classification.

Focused analysis on Markov interval maps.

Abstract

We study continuous countably piecewise monotone interval maps, and formulate conditions under which these are conjugate to maps of constant slope, particularly when this slope is given by the topological entropy of the map. We confine our investigation to the Markov case and phrase our conditions in the terminology of the Vere-Jones classification of infinite matrices.