Result: Thermodynamic formalism for subsystems of expanding Thurston maps and large deviations asymptotics
Title:
Thermodynamic formalism for subsystems of expanding Thurston maps and large deviations asymptotics
Authors:
Source:
Proceedings of the London Mathematical Society. 130
Publication Status:
Preprint
Publisher Information:
Wiley, 2024.
Publication Year:
2024
Subject Terms:
Functional analytic techniques in dynamical systems, zeta functions, (Ruelle-Frobenius) transfer operators, etc, Mathematics - Complex Variables, Expanding holomorphic maps, hyperbolicity, structural stability of holomorphic dynamical systems, Combinatorics and topology in relation with holomorphic dynamical systems, Symbolic dynamics, Primary: 37F10, Secondary: 37D35, 37C30, 37F20, 37F15, 37B99, 57M12, Fuchsian and Kleinian groups as dynamical systems, Dynamical Systems (math.DS), Kleinian groups, Dynamics of complex polynomials, rational maps, entire and meromorphic functions, Fatou and Julia sets, Cannon's conjecture, FOS: Mathematics, Thermodynamic formalism, variational principles, equilibrium states for dynamical systems, Mathematics - Dynamical Systems, Complex Variables (math.CV), expanding Thurston maps, Sullivan's dictionary, Low-dimensional topology of special (e.g., branched) coverings
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
1460-244X
0024-6115
0024-6115
DOI:
10.1112/plms.70019
DOI:
10.48550/arxiv.2312.15822
Access URL:
Rights:
Wiley Online Library User Agreement
arXiv Non-Exclusive Distribution
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....cfe6b0d2c391056aee0b8382627930e9
Database:
OpenAIRE
Further Information
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.