Regular and Chaotic Dynamics

, Volume 22, Issue 1, pp 27–53 | Cite as

Degenerate billiards in celestial mechanics

On the 70th Birthday of Nikolai N. Nekhoroshev Special Memorial Issue. Part 2
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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 

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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.University of Wisconsin-MadisonMadisonUSA
  2. 2.V.A. Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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