For citation:
Loskutov A. J., Akinshin L. G., Sobolevskii A. N. Dynamics of billiards with periodically time-dependent boundaries. Izvestiya VUZ. Applied Nonlinear Dynamics, 2001, vol. 9, iss. 4, pp. 50-63. DOI: 10.18500/0869-6632-2001-9-4-50-63
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Language:
Russian
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Article type:
Article
UDC:
531.19
Dynamics of billiards with periodically time-dependent boundaries
Autors:
Loskutov Aleksandr Jurevich, Lomonosov Moscow State University
Akinshin Leonid Gennadevich, Lomonosov Moscow State University
Sobolevskii Andrei Nikolaevich, Lomonosov Moscow State University
Abstract:
Dynamical systems corresponding to billiards with periodic perturbed boundaries are investigated. A general approach going back to the Aubrey — Mather theory is proposed. On the basis of investigations of the billiard maps, planar billiards with time— dependent boundaries in the form of stadium and circle, and billiards оп two—dimensional sphere with the boundary formed by a disk of the varying radius are considered.
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Acknowledgments:
The authors express their deep gratitude to Prof. Y.G. Sinai, Prof. V.I. Oseledz and Prof. B.M. Gurevich for productive discussions.
Reference:
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Received:
25.04.2001
Accepted:
18.10.2001
Published:
08.02.2002
Journal issue:
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