Homoclinic and heteroclinic intersections for lemon billiards
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866910391144022016 |
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| author | Jin, Xin Zhang, Pengfei |
| author_facet | Jin, Xin Zhang, Pengfei |
| contents | 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 $δ_0>0$ such that for all $b\in(1.5, 1.5+δ_0)$ (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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_06477 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Homoclinic and heteroclinic intersections for lemon billiards Jin, Xin Zhang, Pengfei Dynamical Systems 37C83 37C29 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 $δ_0>0$ such that for all $b\in(1.5, 1.5+δ_0)$ (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. |
| title | Homoclinic and heteroclinic intersections for lemon billiards |
| topic | Dynamical Systems 37C83 37C29 |
| url | https://arxiv.org/abs/2203.06477 |