For every weakly coarse expanding system, every Holder potential has a unique equilibrium state and the system satisfies the central limit theorem, the law of the iterated logarithm, exponential decay of correlations, and large deviations, including on the 2-sphere with periodic critical points.
Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomor phisms, Lecture Notes in Mathematics 470, Springer, 1975
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Thermodynamic formalism for coarse expanding dynamical systems
For every weakly coarse expanding system, every Holder potential has a unique equilibrium state and the system satisfies the central limit theorem, the law of the iterated logarithm, exponential decay of correlations, and large deviations, including on the 2-sphere with periodic critical points.