Ergodic maximization problem for expanding maps with differentiable observables

2020/05/19 by X. Zhang, Zhang, X.
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Topology and Set Theory #Caveolin-1 and cellular processes #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2005.09164

openalex publication_date 2020/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for an expanding map, the maximizing measures of a generic (open and dense) C^r (r∈ℕ) differentiable functions are supported on a single periodic orbit. [There is a gap in the discussions. For the C^∞ approximation of the Lipschitz functions, we can only control the C¹ derivative, but we can not control the C^r derivatives for r≥2. Elegant approximation methods might be needed to solve this problem.]

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