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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 295, Pages 34–40
DOI: https://doi.org/10.1134/S0371968516040026 (Mi tm3748) 		 
This article is cited in 7 scientific papers (total in 7 papers)

On fourth-degree polynomial integrals of the Birkhoff billiard

M. Bialya, A. E. Mironovb

a Tel-Aviv University, Tel Aviv, Israel
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090 Russia
Full-text PDF (166 kB) Citations (7)
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DOI: https://doi.org/10.1134/S0371968516040026
Abstract: We study the Birkhoff billiard in a convex domain with a smooth boundary $\gamma$. 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 $\gamma$ is an ellipse.
Funding agency Grant number
Israel Science Foundation 162/15
Russian Science Foundation 14-11-00441
The work of M. Bialy is supported by the Israel Science Foundation under grant 162/15. The work of A. E. Mironov is supported by the Russian Science Foundation under grant 14-11-00441.
Received: June 14, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 295, Pages 27–32
DOI: https://doi.org/10.1134/S0081543816080022
Bibliographic databases:
Document Type: Article
UDC: 531.01
Language: Russian
Citation: M. Bialy, A. E. Mironov, “On fourth-degree polynomial integrals of the Birkhoff billiard”, Modern problems of mechanics, Collected papers, Trudy Mat. Inst. Steklova, 295, MAIK Nauka/Interperiodica, Moscow, 2016, 34–40; Proc. Steklov Inst. Math., 295 (2016), 27–32
Citation in format AMSBIB
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\vol 295
\pages 34--40
\publ MAIK Nauka/Interperiodica
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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