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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.02093 |
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| _version_ | 1866929611609210880 |
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| author | Villanueva, Carlos Zhang, Pengfei |
| author_facet | Villanueva, Carlos Zhang, Pengfei |
| contents | We investigate the fundamental properties of Minkowski billiards and introduce a new coordinate system $(s,u)$ on the phase space $\mathcal{M}$. In this coordinate system, the Minkowski billiard map $\mathcal{T}$ preserves the standard area form $ω= ds \wedge du$. We then classify the periodic orbits of Minkowski billiards with period $2$ and derive formulas for the twist coefficient $τ_1$ for elliptic periodic orbits, expressed in terms of the geometric characteristics of the billiard table. Additionally, we analyze the stability properties of these elliptic periodic orbits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02093 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twist Coefficients of Periodic Orbits of Minkowski Billiards Villanueva, Carlos Zhang, Pengfei Dynamical Systems We investigate the fundamental properties of Minkowski billiards and introduce a new coordinate system $(s,u)$ on the phase space $\mathcal{M}$. In this coordinate system, the Minkowski billiard map $\mathcal{T}$ preserves the standard area form $ω= ds \wedge du$. We then classify the periodic orbits of Minkowski billiards with period $2$ and derive formulas for the twist coefficient $τ_1$ for elliptic periodic orbits, expressed in terms of the geometric characteristics of the billiard table. Additionally, we analyze the stability properties of these elliptic periodic orbits. |
| title | Twist Coefficients of Periodic Orbits of Minkowski Billiards |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2412.02093 |