Unique ergodicity of asynchronous rotations, and application

2016/09/15 by François Maucourant, Maucourant, François
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1609.04581

openalex publication_date 2016/09/15 · openalex created_date 2025/06/18 · openalex updated_date 2026/07/28

Abstract

The main result of this paper is an analogue for a continuous family of tori of Kronecker-Weyl's unique ergodicity of irrational rotations. We show that the notion corresponding in this setup to irrationality, namely asynchronicity, is satisfied in some homogeneous dynamical systems. This is used to prove the ergodicity of naturals lifts of invariant measures.

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