Equilibrium states for natural extensions of non-uniformly expanding local homeomorphisms. Issue 4 (2nd October 2021)

• Record Type: Journal Article
• Authors: Fisher, Todd; Oliveira, Krerley
• Is Part Of: Dynamical systems. Volume 36:Issue 4(2021)
• Page Start: 685
• Page End: 698
• Publication Date: 2021-10-02
• Subjects: Dynamical systems -- equilibrium states -- attractor -- measures of maximal entropy -- natural extension; 37B40 -- 37C40 -- 37D30; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2021.1983773
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: We examine the uniqueness of equilibrium states for the natural extension of a topologically exact, non-uniformly expanding, local homeomorphism with a Hölder continuous potential function. We do this by applying general techniques developed by Climenhaga and Thompson, and show there is a natural condition on the decompositions which guarantees a unique equilibrium state exists. We then show how to apply these results to certain partially hyperbolic attractors.