Low complexity of optimizing measures over an expanding circle map

2022/06/11 by Rui Gao, Gao, Rui, Weixiao Shen +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2206.05467

openalex publication_date 2022/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that for real analytic expanding circle maps, all optimizing measures of a real analytic potential function have zero entropy, unless the potential is cohomologous to constant. We use the group structure of the symbolic space to solve a transversality problem involved. We also discuss applications to optimizing measures for generic smooth potentials and to Lyapunov optimizing measures.

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