Classical billiards can compute
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908988627484672 |
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| author | Miranda, Eva Ramos, Isaac |
| author_facet | Miranda, Eva Ramos, Isaac |
| contents | We show that two-dimensional billiard systems are Turing complete, in the sense that the halting of any Turing machine with a given input is equivalent to a certain bounded trajectory in this system entering a specified open set. Billiards serve as idealized models of particle motion with elastic reflections and arise naturally as limits of smooth Hamiltonian systems under steep confining potentials. Our results establish the existence of undecidable trajectories in physically natural billiard-type models, including billiard-type models arising in hard-sphere gases and in collision-chain limits of celestial mechanics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19156 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classical billiards can compute Miranda, Eva Ramos, Isaac Dynamical Systems Computational Complexity Mathematical Physics We show that two-dimensional billiard systems are Turing complete, in the sense that the halting of any Turing machine with a given input is equivalent to a certain bounded trajectory in this system entering a specified open set. Billiards serve as idealized models of particle motion with elastic reflections and arise naturally as limits of smooth Hamiltonian systems under steep confining potentials. Our results establish the existence of undecidable trajectories in physically natural billiard-type models, including billiard-type models arising in hard-sphere gases and in collision-chain limits of celestial mechanics. |
| title | Classical billiards can compute |
| topic | Dynamical Systems Computational Complexity Mathematical Physics |
| url | https://arxiv.org/abs/2512.19156 |