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Zapiski Nauchnykh Seminarov POMI, 2003, Volume 300, Pages 56–64
(Mi znsl962)
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This article is cited in 7 scientific papers (total in 7 papers)
Billiards and nonholonomic distributions
Y. Baryshnikov, V. Zharnitsky Alcatel-Lucent Bell Labs
Abstract:
In this note, billiards with full families of periodic orbits are considered. It is shown that construction of a convex billiard with a “rational” caustic (i.e., carrying only periodic orbits) can be reformulated as a problem of finding a closed curve tangent to a $(N-1)$-dimensional distribution on a $(2N-1)$-dimensional manifold. The properties of this distribution are described as well as some important consequences for the billiards with rational caustics. A very particular application of our construction states that an ellipse can be infinitesimally perturbed so that any chosen rational elliptic caustic will persist.
Received: 30.11.2002
Citation:
Y. Baryshnikov, V. Zharnitsky, “Billiards and nonholonomic distributions”, Representation theory, dynamical systems. Part VIII, Special issue, Zap. Nauchn. Sem. POMI, 300, POMI, St. Petersburg, 2003, 56–64; J. Math. Sci. (N. Y.), 128:2 (2005), 2706–2710
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https://www.mathnet.ru/eng/znsl962 https://www.mathnet.ru/eng/znsl/v300/p56
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Abstract page: | 209 | Full-text PDF : | 91 | References: | 43 |
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