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

2018/10/04 by Azam Ehsani, Abbas Fakhari, Ehsani, A. +4
Mathematics · #Advanced Topology and Set Theory #Combinatorics #Computer science #Countable set #Discrete mathematics #Dynamical Systems (math.DS) #Ergodic theory #FOS: Mathematics #Krohn–Rhodes theory #Markov chain #Mathematical Dynamics and Fractals #Mathematics #Partition (number theory) #Physics #Pure mathematics #Semigroup #Skew #Special classes of semigroups #Statistical physics #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1810.02299

openalex publication_date 2018/10/04 · openalex created_date 2020/12/07 · openalex updated_date 2026/08/05

Abstract

For topologically mixing locally conformal semigroup actions generated by a finite collection of C^1+α 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.

Citations

• Recurrence times and rates of mixing
• GIBBS MEASURES IN ERGODIC THEORY
• Markov maps associated with fuchsian groups

Related

• Thermodynamic Formalism for Generalized Markov Shifts on Infinitely Many States
• Central limit theorem for dimension of Gibbs measures for skew expanding maps
• Uniqueness of conformal measures and local mixing for Anosov groups
• Exponential mixing for Gibbs measures on self-conformal sets and applications
• Ergodicity of non-autonomous discrete systems with non-uniform expansion