Constant Slope Models for Finitely Generated Maps

TL;DR

This paper investigates conditions under which countably monotone and Markov interval maps can be uniquely conjugated to constant slope models, using global window perturbation to generate such maps.

Contribution

It provides new sufficient conditions for the uniqueness of conjugate maps of constant slope and introduces a method to generate maps satisfying these conditions.

Findings

Established conditions for uniqueness of conjugate maps of constant slope.

Showed how global window perturbation can generate maps meeting these conditions.

Expanded understanding of the structure of countably monotone and Markov interval maps.

Abstract

We study countably monotone and Markov interval maps. We establish sufficient conditions for uniqueness of a conjugate map of constant slope. We explain how global window perturbation can be used to generate a large class of maps satisfying these conditions.