Email this article On fourth-degree polynomial integrals of the Birkhoff billiard
- Authors: Bialy M.1, Mironov A.E.2
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Affiliations:
- Tel-Aviv University
- Sobolev Institute of Mathematics
- Issue: Vol 295, No 1 (2016)
- Pages: 27-32
- Section: Article
- URL: https://journals.rcsi.science/0081-5438/article/view/174120
- DOI: https://doi.org/10.1134/S0081543816080022
- ID: 174120
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Abstract
We study the Birkhoff billiard in a convex domain with a smooth boundary γ. We show that if this dynamical system has an integral which is polynomial in velocities of degree 4 and is independent with the velocity norm, then γ is an ellipse.
About the authors
M. Bialy
Tel-Aviv University
Author for correspondence.
Email: bialy@post.tau.ac.il
Israel, Tel Aviv
A. E. Mironov
Sobolev Institute of Mathematics
Email: bialy@post.tau.ac.il
Russian Federation, pr. Akademika Koptyuga 4, Novosibirsk, 630090
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