Elliptic islands and zero measure escaping orbits in a class of outer billiards
Dynamical Systems
2025-06-24 v1
Abstract
We study outer billiard systems around a class of circular sectors. For semi-discs, we prove the existence of elliptic islands occupying a positive proportion of the plane. Combined with known results, this shows the coexistence of stability and diffusion for this system. On the other hand, we show that there exists a countable family of circular sectors for which the outer billiard system has zero measure of escaping orbits.
Cite
@article{arxiv.2506.18433,
title = {Elliptic islands and zero measure escaping orbits in a class of outer billiards},
author = {Zaicun Li},
journal= {arXiv preprint arXiv:2506.18433},
year = {2025}
}