Classification of billiard motions in domains bounded by confocal parabolas
- M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
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.
- OSTI ID:
- 22364914
- Journal Information:
- Sbornik. Mathematics, Vol. 205, Issue 8; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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