RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Guidelines for authors License agreement Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy MIAN: Year: Volume: Issue: Page: Find

 Tr. Mat. Inst. Steklova, 2016, Volume 295, Pages 53–71 (Mi tm3747)

Degenerate billiards

S. V. Bolotin

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

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.

DOI: https://doi.org/10.1134/S037196851604004X

Full text: PDF file (283 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 295, 45–62

Bibliographic databases:

UDC: 531.01

Citation: S. V. Bolotin, “Degenerate billiards”, Modern problems of mechanics, Collected papers, Tr. Mat. Inst. Steklova, 295, MAIK Nauka/Interperiodica, Moscow, 2016, 53–71; Proc. Steklov Inst. Math., 295 (2016), 45–62

Citation in format AMSBIB
\Bibitem{Bol16} \by S.~V.~Bolotin \paper Degenerate billiards \inbook Modern problems of mechanics \bookinfo Collected papers \serial Tr. Mat. Inst. Steklova \yr 2016 \vol 295 \pages 53--71 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3747} \crossref{https://doi.org/10.1134/S037196851604004X} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3628514} \elib{http://elibrary.ru/item.asp?id=27643602} \transl \jour Proc. Steklov Inst. Math. \yr 2016 \vol 295 \pages 45--62 \crossref{https://doi.org/10.1134/S0081543816080046} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000395572400004} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85010767528} 

• http://mi.mathnet.ru/eng/tm3747
• https://doi.org/10.1134/S037196851604004X
• http://mi.mathnet.ru/eng/tm/v295/p53

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Sergey V. Bolotin, “Degenerate Billiards in Celestial Mechanics”, Regul. Chaotic Dyn., 22:1 (2017), 27–53
2. S. V. Bolotin, V. V. Kozlov, “Topological approach to the generalized $n$-centre problem”, Russian Math. Surveys, 72:3 (2017), 451–478
3. J. Fejoz, A. Knauf, R. Montgomery, “Lagrangian relations and linear point billiards”, Nonlinearity, 30:4 (2017), 1326–1355
•  Number of views: This page: 173 References: 17 First page: 10