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arXiv · 1908.08270

Thermodynamic formalism for coarse expanding dynamical systems

Tushar Das·Feliks Przytycki·Giulio Tiozzo·Mariusz Urbanski·Anna Zdunik
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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.

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Tushar Das, Feliks Przytycki, Giulio Tiozzo, Mariusz Urbanski, Anna Zdunik. 2019-08-22. Thermodynamic formalism for coarse expanding dynamical systems. https://doi.org/10.1007/s00220-021-04058-2

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