Thermodynamic formalism for coarse expanding dynamical systems
Dynamical Systems
2022-11-29 v3
Abstract
We consider a class of dynamical systems, which we call weakly coarse expanding, which is a generalization to the postcritically infinite case of expanding Thurston maps as discussed by Bonk-Meyer and is closely related to coarse expanding conformal systems as defined by Haissinsky-Pilgrim. We prove existence and uniqueness of equilibrium states for a wide class of potentials, as well as statistical laws such as a central limit theorem, law of iterated logarithm, exponential decay of correlations and a large deviation principle. Further, if the system is defined on the 2-sphere, we prove all such results even in presence of periodic (repelling) branch points.
Cite
@article{arxiv.1908.08270,
title = {Thermodynamic formalism for coarse expanding dynamical systems},
author = {Tushar Das and Feliks Przytycki and Giulio Tiozzo and Mariusz Urbanski and Anna Zdunik},
journal= {arXiv preprint arXiv:1908.08270},
year = {2022}
}
Comments
30 pages, revised version