Billiard Trajectories inside Cones Full article
| Journal |
Regular and Chaotic Dynamics
ISSN: 1560-3547 , E-ISSN: 1468-4845 |
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| Output data | Year: 2025, Volume: 30, Number: 4, Pages: 688-710 Pages count : 23 DOI: 10.1134/s156035472504015x | ||
| Tags | Birkhoff billiards, cone billiards | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования РФ | 075-15-2025-348 |
Abstract:
Recently it was proved that every billiard trajectory inside a C3 convex cone has a finite number of reflections. Here, by a C3 convex cone, we mean a cone whose section with some hyperplane is a strictly convex, closed C3 hypersurface of that hyperplane, with an everywhere nondegenerate second fundamental form. In this paper, we prove that there exist C2 convex cones with billiard trajectories that undergo infinitely many reflections in finite time. We also provide an estimation of the number of reflections for billiard trajectories inside elliptic cones in R3 using two first integrals.
Cite:
Mironov A.E.
, Yin S.
Billiard Trajectories inside Cones
Regular and Chaotic Dynamics. 2025. V.30. N4. P.688-710. DOI: 10.1134/s156035472504015x WOS Scopus РИНЦ OpenAlex
Billiard Trajectories inside Cones
Regular and Chaotic Dynamics. 2025. V.30. N4. P.688-710. DOI: 10.1134/s156035472504015x WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Apr 30, 2025 |
| Accepted: | Jun 11, 2025 |
| Published print: | Aug 11, 2025 |
| Published online: | Aug 11, 2025 |
Identifiers:
| Web of science: | WOS:001548326100014 |
| Scopus: | 2-s2.0-105013022662 |
| Elibrary: | 82740655 |
| OpenAlex: | W4413210661 |
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