Effective uniqueness of Parry measure and exceptional sets in ergodic theory

2014/09/03 by Shirali Kadyrov, Kadyrov, Shirali
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1409.0946

openalex publication_date 2014/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that hyperbolic dynamical systems admit a unique invariant probability measure with maximal entropy. We prove an effective version of this statement and use it to estimate an upper bound for Hausdorff dimension of exceptional sets arising from dynamics.

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