Thermodynamic formalism for subsystems of expanding Thurston maps and large deviations asymptotics
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917880259411968 |
|---|---|
| author | Li, Zhiqiang Shi, Xianghui Zhang, Yiwei |
| author_facet | Li, Zhiqiang Shi, Xianghui Zhang, Yiwei |
| contents | Expanding Thurston maps were introduced by M. Bonk and D. 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 $S^{2}$ is equipped with a natural metric, called a visual metric, introduced by M. Bonk and D. Meyer. As an application, we establish large deviation asymptotics for expanding Thurston maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15822 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Thermodynamic formalism for subsystems of expanding Thurston maps and large deviations asymptotics Li, Zhiqiang Shi, Xianghui Zhang, Yiwei Dynamical Systems Complex Variables Primary: 37F10, Secondary: 37D35, 37C30, 37F20, 37F15, 37B99, 57M12 Expanding Thurston maps were introduced by M. Bonk and D. 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 $S^{2}$ is equipped with a natural metric, called a visual metric, introduced by M. Bonk and D. Meyer. As an application, we establish large deviation asymptotics for expanding Thurston maps. |
| title | Thermodynamic formalism for subsystems of expanding Thurston maps and large deviations asymptotics |
| topic | Dynamical Systems Complex Variables Primary: 37F10, Secondary: 37D35, 37C30, 37F20, 37F15, 37B99, 57M12 |
| url | https://arxiv.org/abs/2312.15822 |