Degenerate Billiards in Celestial Mechanics

    2017, Volume 22, Number 1, pp.  27-53

    Author(s): Bolotin S. V.

    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
    Citation: Bolotin S. V., Degenerate Billiards in Celestial Mechanics, Regular and Chaotic Dynamics, 2017, Volume 22, Number 1, pp. 27-53

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