Invariant Conditional Expectations and Unique Ergodicity for Anzai Skew-Products

2021/08/26 by Simone Del Vecchio, Del Vecchio, Simone, Francesco Fidaleo +3
Mathematics · Physics and Astronomy · #37A05 #37A55 #37B05 #46L30 #FOS: Mathematics #Functional Analysis (math.FA) #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Operator Algebras (math.OA) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2108.11938

openalex publication_date 2021/08/26 · openalex created_date 2022/11/25 · openalex updated_date 2026/07/28

Abstract

Anzai skew-products are shown to be uniquely ergodic with respect to the fixed-point subalgebra if and only if there is a unique conditional expectation onto such a subalgebra which is invariant under the dynamics. For the particular case of skew-products, this solves a question raised by B. Abadie and K. Dykema in the wider context of C^*-dynamical systems.

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