Higher order terms of Mather's β-function for symplectic and outer billiards

2024/03/25 by Luca Baracco, Olga Bernardi, Alessandra Nardi · 6 citations
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Mathematical Dynamics and Fractals #Scientific Research and Discoveries

paper · doi:10.1016/j.jmaa.2024.128353

Abstract

We compute explicitly the formal Taylor expansion of Mather's β-function up to seventh order terms for symplectic and outer billiards in a strictly-convex planar domain C. In particular, we specify the third terms of the asymptotic expansions of the distance (in the sense of the symmetric difference metric) between C and its best approximating inscribed or circumscribed polygons with at most n vertices. We use tools from affine differential geometry.

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• Birkhoff attractors for dissipative symplectic billiards
• Isoperimetric-type inequalities for Mather's β-function of convex billiards

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