Equilibrium States for Piecewise Weakly Convex Interval Maps

TL;DR

This paper establishes the existence and conditions for uniqueness of equilibrium states in a class of piecewise weakly convex interval maps, including systems with indifferent fixed points and non-Markov partitions.

Contribution

It proves the existence of equilibrium states for geometric potentials in these complex interval maps, extending previous results to broader classes.

Findings

Existence of equilibrium states for geometric potentials in the class.

Conditions under which uniqueness of equilibrium states is guaranteed.

Applicable to systems with indifferent fixed points and non-Markov partitions.

Abstract

We prove the existence of equilibrium states for geometric potentials in a class of piecewise weakly convex interval maps. This class includes systems with indifferent fixed points and non-Markov partitions. Under additional hypotheses we also obtain uniqueness.