Homoclinic and heteroclinic intersections for lemon billiards

Abstract

We study the dynamical billiards on a symmetric lemon table $\mathcal{Q}(b)$, where $\mathcal{Q}(b)$ is the intersection of two unit disks with center distance $b$. We show that there exists ${\delta }_0>0$ such that for all $b\in (1.5,1.5+{\delta }_0)$ (except possibly a discrete subset), the billiard map $F_b$ on the lemon table $\mathcal{Q}(b)$ admits crossing homoclinic and heteroclinic intersections. In particular, such lemon billiards have positive topological entropy.

arXiv commentFinal version. To appear on the journal Advances in Mathematics

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