Work

Thermodynamic formalism for subsystems of expanding Thurston maps and large deviations asymptotics

Year: 2024

Type: article

Abstract: Expanding Thurston maps were introduced by Bonk and Meyer with motivation from complex dynamics and Cannon's conjecture from geometric group theory via Sullivan's dictionary. In this paper, we introduce subsystems of expanding Thurston maps motivated via Sullivan's dictionary as analogs of some subgroups of Kleinian groups. We use thermodynamic formalism to prove the Variational Principle and the existence of equilibrium states for strongly irreducible subsystems and real‐valued Hölder continuous potentials. Here, the sphere is equipped with a natural metric, called a visual metric, introduced by Bonk and Meyer. As an application, we establish large deviation asymptotics for expanding Thurston maps.

Source: Proceedings of the London Mathematical Society

DOI: 10.1112/plms.70019

Authors: Zhiqiang Li, Xianghui Shi, Yiwei Zhang

Institutions: Peking University, Anhui University of Science and Technology

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Natural Science Foundation of China