Entropies of commuting transformations on Hilbert spaces

2020/06/15 by Zhiming Li, Li, Zhiming, Yujun Zhu +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #advanced mathematical theories #math.DS #math.FA

paper · pdf · doi:10.48550/arxiv.2006.08077

arxiv created 2020/06/15 · openalex publication_date 2020/06/15 · arxiv updated 2020/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By establishing Multiplicative Ergodic Theorem for commutative transformations on a separable infinite dimensional Hilbert space, in this paper, we investigate Pesin's entropy formula and SRB measures of a finitely generated random transformations on such space via its commuting generators. Moreover, as an application, we give a formula of Friedland's entropy for certain C² ℕ²-actions.

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