Keplerian billiards in three dimensions: stability of equilibrium orbits and conditions for chaos
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909357636059136 |
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| author | De Blasi, Irene |
| author_facet | De Blasi, Irene |
| contents | This work presents some results regarding three-dimensional billiards having a non-constant potential of Keplerian type inside a regular domain $D\subset \mathcal R^3$. Two models will be analysed: in the first one, only an inner Keplerian potential is present, and every time the particle encounters the boundary of $D$ is reflected back by keeping constant its tangential component to $\partial D$. The second model is a refractive billiard, where the inner Keplerian potential is coupled with a harmonic outer one; in this case, the interaction with $\partial D$ results in a generalised refraction Snell's law. In both cases, the analysis of a particular type of straight equilibrium trajectories, called \emph{homothetic}, is carried on, and their presence is linked to the topological chaoticity of the dynamics for large inner energies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15935 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Keplerian billiards in three dimensions: stability of equilibrium orbits and conditions for chaos De Blasi, Irene Chaotic Dynamics 34C28, 70F15, 37C83, 70F16 This work presents some results regarding three-dimensional billiards having a non-constant potential of Keplerian type inside a regular domain $D\subset \mathcal R^3$. Two models will be analysed: in the first one, only an inner Keplerian potential is present, and every time the particle encounters the boundary of $D$ is reflected back by keeping constant its tangential component to $\partial D$. The second model is a refractive billiard, where the inner Keplerian potential is coupled with a harmonic outer one; in this case, the interaction with $\partial D$ results in a generalised refraction Snell's law. In both cases, the analysis of a particular type of straight equilibrium trajectories, called \emph{homothetic}, is carried on, and their presence is linked to the topological chaoticity of the dynamics for large inner energies. |
| title | Keplerian billiards in three dimensions: stability of equilibrium orbits and conditions for chaos |
| topic | Chaotic Dynamics 34C28, 70F15, 37C83, 70F16 |
| url | https://arxiv.org/abs/2410.15935 |