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arXiv · 2504.11915

Starting the study of outer length billiards

Luca Baracco·Olga Bernardi·Corentin Fierobe
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Abstract

We focus on the outer length billiard dynamics, acting on the exterior of a strictly-convex planar domain. We first show that ellipses are totally integrable. We then provide an explicit representation of first order terms for the formal Taylor expansion of the corresponding Mather's $\beta$-function. Finally, we provide explicit Lazutkin coordinates up to order 4.

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Luca Baracco, Olga Bernardi, Corentin Fierobe. 2025-04-16. Starting the study of outer length billiards. https://doi.org/10.2140/pjm.2025.339.201

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