Ergodization time for linear flows on tori via geometry of numbers
Abed Bounemoura (UCI)
TL;DR
This paper presents a new geometric proof for the optimal ergodization time of linear flows on tori, improving understanding through geometry of numbers instead of Fourier analysis.
Contribution
It introduces a simple geometric proof based on Diophantine duality, providing an alternative to Fourier analysis for this problem.
Findings
Provides a shorter, more intuitive proof of ergodization time
Utilizes geometry of numbers and Diophantine duality
Confirms the optimality of ergodization time for linear flows
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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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Geometric and Algebraic Topology