Work

Equilibrium measures for two-sided shift spaces via dimension theory

Year: 2024

Type: article

Abstract: Given a two-sided shift space on a finite alphabet and a continuous potential function, we give conditions under which an equilibrium measure can be described using a construction analogous to Hausdorff measure that goes back to the work of Bowen. This construction was previously applied to smooth uniformly and partially hyperbolic systems by the first author, Pesin, and Zelerowicz. Our results here apply to all subshifts of finite type and Hölder continuous potentials, but extend beyond this setting, and we also apply them to shift spaces with synchronizing words.

Source: Ergodic Theory and Dynamical Systems

DOI: 10.1017/etds.2024.46

Authors: VAUGHN CLIMENHAGA, JASON DAY

Institution: University of Houston

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Simons Foundation, Division of Mathematical Sciences

Awards: CAREER: Unifying approaches to non-uniform hyperbolicity, G3819841463, Hyperbolicity with Singularities and Coexistence via Smoothing, G5415602535