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Thermodynamics via Inducing
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Thermodynamics via Inducing
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Journal Article
Thermodynamics via Inducing
2019
Overview
We consider continuous maps f:X→X on compact metric spaces admitting inducing schemes of hyperbolic type introduced in Pesin et al. (Trans Amer Math Soc 368(12):8519–8552, 2016) as well as the induced maps f~:X~→X~ and the associated tower maps f^:X^→X^ . For a certain class of potential functions φ on X, which includes all Hölder continuous functions, we establish thermodynamic formalism for each of the above three systems and we describe some relations between the corresponding equilibrium measures. Furthermore we study ergodic properties of these equilibrium measures including the Bernoulli property, decay of correlations, and the Central Limit Theorem. Finally, we prove analyticity of the pressure function for the three systems.
Publisher
Springer Nature B.V
