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arXiv · 2311.01121

Higher order terms of Mather's $\beta$-function for symplectic and outer billiards

Luca Baracco·Olga Bernardi·Alessandra Nardi
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Abstract

We compute explicitly the higher order terms of the formal Taylor expansion of Mather's $\beta$-function 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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Luca Baracco, Olga Bernardi, Alessandra Nardi. 2023-11-02. Higher order terms of Mather's $\beta$-function for symplectic and outer billiards. https://arxiv.org/abs/2311.01121

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