Thermodynamic formalism for subsystems of expanding Thurston maps II

Source abstract

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 series of two papers, including Li et al. [Proc. London Math. Soc. (3) 130 (2025), Paper No. e70019], we develop the thermodynamic formalism for subsystems of expanding Thurston maps. In this paper, we prove the uniqueness and various ergodic properties of the equilibrium state for a strongly primitive subsystem and a real‐valued Hölder continuous potential, and establish the equidistribution of preimages of the subsystem with respect to the equilibrium state. As a result, for a strongly primitive subsystem of an expanding Thurston map without periodic critical points, we obtain level‐2 large deviation principles for the distributions of Birkhoff averages and iterated preimages.