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Regul. Chaotic Dyn., 2017, Volume 22, Issue 1, Pages 27–53 (Mi rcd242)  

Degenerate Billiards in Celestial Mechanics

Sergey V. Bolotinab

a University of Wisconsin-Madison, 480 Lincoln Dr., Madison, WI 53706-1325, USA
b V.A. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: In an ordinary billiard trajectories of a Hamiltonian system are elastically reflected after a collision with a hypersurface (scatterer). If the scatterer is a submanifold of codimension more than one, we say that the billiard is degenerate. Degenerate billiards appear as limits of systems with singularities in celestial mechanics. We prove the existence of trajectories of such systems shadowing trajectories of the corresponding degenerate billiards. This research is motivated by the problem of second species solutions of Poincaré.

Keywords: Hamiltonian system, billiard, celestial mechanics, collision, regularization, shadowing, action functional

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-03747a
Supported by the RFBR grant of the Russian Academy of Sciences “Modern problems of classical dynamics” (project 15-01-03747a).


DOI: https://doi.org/10.1134/S1560354717010038

References: PDF file   HTML file

Bibliographic databases:

MSC: 37D05, 37D50, 37J15, 37J50, 37N05
Received: 29.11.2016
Accepted:06.12.2016
Language:

Citation: Sergey V. Bolotin, “Degenerate Billiards in Celestial Mechanics”, Regul. Chaotic Dyn., 22:1 (2017), 27–53

Citation in format AMSBIB
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\paper Degenerate Billiards in Celestial Mechanics
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\vol 22
\issue 1
\pages 27--53
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