Thermodynamic Formalism for Coarse Expanding Dynamical Systems

We consider a class of dynamical systems, which we call weakly coarse expanding, is generalization to the postcritically infinite case expanding Thurston maps as discussed by Bonk-Meyer and closely related conformal systems defined Haissinsky-Pilgrim. prove existence uniqueness equilibrium states for wide potentials, well statistical laws such central limit theorem, law iterated logarithm, exponential decay correlations large deviation principle. Further, if system on 2-sphere, all results even in presence periodic (repelling) branch points.