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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 295, Pages 53–71
DOI: https://doi.org/10.1134/S037196851604004X (Mi tm3747) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Degenerate billiards

S. V. Bolotin

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Full-text PDF (283 kB) Citations (9)
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DOI: https://doi.org/10.1134/S037196851604004X
Abstract: In an ordinary billiard system, trajectories of a Hamiltonian system are elastically reflected after a collision with a hypersurface (scatterer). If the scatterer is a submanifold of codimension more than $1$, we say that the billiard is degenerate. We study those trajectories of degenerate billiards that have an infinite number of collisions with the scatterer. Degenerate billiards appear as limits of systems with elastic reflections or as small-mass limits of systems with singularities in celestial mechanics. We prove the existence of trajectories of such systems that shadow the trajectories of the corresponding degenerate billiards. The proofs are based on a version of the method of an anti-integrable limit.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.
Received: June 22, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 295, Pages 45–62
DOI: https://doi.org/10.1134/S0081543816080046
Bibliographic databases:
Document Type: Article
UDC: 531.01
Language: Russian
Citation: S. V. Bolotin, “Degenerate billiards”, Modern problems of mechanics, Collected papers, Trudy Mat. Inst. Steklova, 295, MAIK Nauka/Interperiodica, Moscow, 2016, 53–71; Proc. Steklov Inst. Math., 295 (2016), 45–62
Citation in format AMSBIB
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\pages 53--71
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    • This publication is cited in the following 9 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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