Birkhoff Normal Form and Twist Coefficients of Periodic Orbits of Billiards
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866911819628544000 |
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| author | Jin, Xin Zhang, Pengfei |
| author_facet | Jin, Xin Zhang, Pengfei |
| contents | In this paper we study the Birkhoff Normal Form around elliptic periodic points for a variety of dynamical billiards. We give an explicit construction of the Birkhoff transformation and obtain explicit formulas for the first two twist coefficients in terms of the geometric parameters of the billiard table. As an application, we obtain characterizations of the nonlinear stability and local analytic integrability of the billiards around the elliptic periodic points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_12098 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Birkhoff Normal Form and Twist Coefficients of Periodic Orbits of Billiards Jin, Xin Zhang, Pengfei Dynamical Systems 37G05 37C83 37E40 In this paper we study the Birkhoff Normal Form around elliptic periodic points for a variety of dynamical billiards. We give an explicit construction of the Birkhoff transformation and obtain explicit formulas for the first two twist coefficients in terms of the geometric parameters of the billiard table. As an application, we obtain characterizations of the nonlinear stability and local analytic integrability of the billiards around the elliptic periodic points. |
| title | Birkhoff Normal Form and Twist Coefficients of Periodic Orbits of Billiards |
| topic | Dynamical Systems 37G05 37C83 37E40 |
| url | https://arxiv.org/abs/2108.12098 |