Ergodization time for linear flows on tori via geometry of numbers

2015/06/22 by Abed Bounemoura, Bounemoura, Abed
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS

paper · pdf · doi:10.48550/arxiv.1506.06469

arxiv created 2015/06/22 · openalex publication_date 2015/06/22 · arxiv updated 2015/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give a new, short, simple and geometric proof of the optimal er-godization time for linear flows on tori. This result was first obtained by Bourgain, Golse and Wennberg in [BGW98] using Fourier analysis. Our proof uses geometry of numbers: it follows trivially from a Diophantine duality that was established by the author and Fischler in [BF13].

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