Locally conformal expanding Actions: Markov Partition and Thermodynamic of the induced skew product

Abstract: For topologically mixing locally conformal semigroup actions generated by a finite collection of $C^{1+\alpha}$ conformal local diffeomorphisms, we provide a countable Markov partition satisfying the finite images and the finite cycle properties. We show that they admit inducing schemes and describe the tower constructions associated with them. An important feature of these towers is that their induced maps are equivalent to a subshift of countable type. Through the investigating the ergodic properties of induced map, we prove the existence of liftable measures and establish a thermodynamic formalism of the induced skew product with respect to them.