Birkhoff billiards inside cones Full article
| Journal |
Advances in Mathematics
ISSN: 0001-8708 , E-ISSN: 1090-2082 |
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| Output data | Year: 2026, Volume: 501, Article number : 111101, Pages count : 1 DOI: 10.1016/j.aim.2026.111101 | ||
| Tags | Birkhoff billiard; billiard integrals | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования РФ | 075-15-2025-348 |
Abstract:
In this paper we study the Birkhoff billiards inside cones in Rn. We prove that every trajectory inside a cone over a C3 strictly convex closed hypersurface embedded in Rn−1 with nondegenerate second fundamental form has a finite number of reflections. Using this result we prove that the billiard admits first integrals whose values uniquely determine all billiard trajectories.
Cite:
Mironov A.E.
, Yin S.
Birkhoff billiards inside cones
Advances in Mathematics. 2026. V.501. 111101 :1-1. DOI: 10.1016/j.aim.2026.111101 OpenAlex
Birkhoff billiards inside cones
Advances in Mathematics. 2026. V.501. 111101 :1-1. DOI: 10.1016/j.aim.2026.111101 OpenAlex
Dates:
| Submitted: | May 6, 2025 |
| Accepted: | Jun 8, 2026 |
| Published online: | Jun 22, 2026 |
Identifiers:
| ≡ OpenAlex: | W7164820934 |