We focus on 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 β-function. Finally, we provide explicit Lazutkin coordinates up to order 4.
Starting the study of outer length billiards
Luca Baracco;Olga Bernardi;
2025
Abstract
We focus on 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 β-function. Finally, we provide explicit Lazutkin coordinates up to order 4.
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