Constant Slope Maps and the Vere-Jones Classification

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.

Keywords

• interval map
• topological entropy
• conjugacy
• constant slope