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This article is cited in 25 scientific papers (total in 25 papers)
Classification of billiard motions in domains bounded by confocal parabolas
V. V. Fokicheva M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
We consider the billiard dynamical system in a domain bounded by confocal parabolas. We describe such domains in which the billiard problem can be correctly stated. In each such domain we prove the integrability for the system,
analyse the arising Liouville foliation, and calculate the invariant of Liouville equivalence — the so-called marked
molecule. It turns out that billiard systems in certain parabolic domains have the same closures of solutions
(integral trajectories) as the systems of Goryachev-Chaplygin-Sretenskii and Joukowski at suitable energy levels. We also describe the billiard motion in noncompact domains bounded by confocal parabolas, namely, we describe the topology of the Liouville foliation in terms of rough molecules.
Bibliography: 16 titles.
Keywords:
integrable system, billiard, Liouville equivalence, Fomenko-Zieschang molecule.
Received: 17.03.2014
Citation:
V. V. Fokicheva, “Classification of billiard motions in domains bounded by confocal parabolas”, Mat. Sb., 205:8 (2014), 139–160; Sb. Math., 205:8 (2014), 1201–1221
Linking options:
https://www.mathnet.ru/eng/sm8359https://doi.org/10.1070/SM2014v205n08ABEH004415 https://www.mathnet.ru/eng/sm/v205/i8/p139
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Abstract page: | 569 | Russian version PDF: | 220 | English version PDF: | 12 | References: | 73 | First page: | 26 |
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