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Regular and Chaotic Dynamics, 2005, Volume 10, Issue 3, Pages 285–306
DOI: https://doi.org/10.1070/RD2005v010n03ABEH000316 (Mi rcd711) 		 
This article is cited in 1 scientific paper (total in 1 paper)

150th anniversary of H. Poincaré

Generalized billiards inside an infinite strip with periodic laws of reflection along the strip's boundaries

S. Albeverioabc, G. Galperind, I. L. Nizhnike, L. P. Nizhnike

a Institute für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, D 53155 Bonn, Germany
b Research Center Bielefeld-Bonn-Stochastics (BiBoS), D-33501 Bielefeld; D-53115 Bonn, Germany
c Research Center for Mathematics and Physics (CERFIM), CH - 6601 Locarno, Switzerland
d Eastern Illinois University, 600 Lincoln Ave., Charleston, IL 61920, USA
e Institute of Mathematics, 3 Tereshchenkivska, Kiev 01601, Ukraine
Citations (1)
DOI: https://doi.org/10.1070/RD2005v010n03ABEH000316
Abstract: A constructive description of generalized billiards is given, the billiards being inside an infinite strip with a periodic law of reflection off the strip's bottom and top boundaries. Each of the boundaries is equipped with the same periodic lattice, where the number of lattice's nodes between any two successive reflection points may be prescribed arbitrarily. For such billiards, a full description of the structure of the set of billiard trajectories is provided, the existence of spatial chaos is found, and the exact value of the spatial entropy in the class of monotonic billiard trajectories is found.
Keywords: billiards, dynamical systems, spatial chaos, entropy.
Received: 13.08.2004
Accepted: 12.01.2005
Bibliographic databases:
Document Type: Article
MSC: 37D50, 37D45,37B10
Language: English
Citation: S. Albeverio, G. Galperin, I. L. Nizhnik, L. P. Nizhnik, “Generalized billiards inside an infinite strip with periodic laws of reflection along the strip's boundaries”, Regul. Chaotic Dyn., 10:3 (2005), 285–306
Citation in format AMSBIB
\Bibitem{AlbGalNiz05}
\by S. Albeverio, G. Galperin, I. L. Nizhnik, L. P. Nizhnik
\paper Generalized billiards inside an infinite strip with periodic laws of reflection along the strip's boundaries
\jour Regul. Chaotic Dyn.
\yr 2005
\vol 10
\issue 3
\pages 285--306
\mathnet{http://mi.mathnet.ru/rcd711}
\crossref{https://doi.org/10.1070/RD2005v010n03ABEH000316}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2155188}
\zmath{https://zbmath.org/?q=an:1076.37021}
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  • https://www.mathnet.ru/eng/rcd/v10/i3/p285
    • This publication is cited in the following 1 articles:
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