Diffusion rate of windtree models and Lyapunov exponents

2018/03/28 by Charles Fougeron, Fougeron, Charles
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1803.10717

openalex publication_date 2018/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a windtree model with several parallel arbitrary right-angled obstacles placed periodically on the plane. We show that its diffusion rate is the largest Lyapunov exponent of some stratum of quadratic differentials and exhibit a new general strategy to compute the generic diffusion rate of such models. This result enables us to compute numerically the diffusion rates of a large family of models, and to observe its asymptotic behaviour according to the shape of the obstacles.

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