English

Starting the study of outer length billiards

Dynamical Systems 2025-09-24 v1

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 β\beta-function. Finally, we provide explicit Lazutkin coordinates up to order 4.

Keywords

Cite

@article{arxiv.2504.11915,
  title  = {Starting the study of outer length billiards},
  author = {Luca Baracco and Olga Bernardi and Corentin Fierobe},
  journal= {arXiv preprint arXiv:2504.11915},
  year   = {2025}
}
R2 v1 2026-06-28T23:00:16.955Z