Existence and Ergodic properties of equilibrium measures for maps associated with inducing schemes of hyperbolic type

Farruh Shahidi, Agnieszka Zelerowicz

Published 2018-03-19Version 1

We consider maps $f:X\to X$ admitting inducing schemes of hyperbolic type introduced in \cite{ind} as well as the induced maps $\tilde{f}:\tilde{X}\to \tilde{X}$ and the associated tower maps $\hat{f}:\hat{X} \to \hat {X}$. For a certain class of potential functions $\varphi$ on $X$, that includes all H\"older continuous functions, we establish thermodynamic formalism for the above three systems. We study relations among the corresponding equilibrium measures and their ergodic properties. We establish decay of correlations, the Central Limit Theorem (CLT), the Bernoulli property for the three systems with respect to their corresponding equilibrium measures. Finally, we prove analyticity of the pressure function for the three systems.