Degenerate billiards in celestial mechanics
Dynamical Systems
2017-03-08 v1
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 Poincar\'e.
Cite
@article{arxiv.1612.08907,
title = {Degenerate billiards in celestial mechanics},
author = {Sergey Bolotin},
journal= {arXiv preprint arXiv:1612.08907},
year = {2017}
}
Comments
arXiv admin note: text overlap with arXiv:1606.06708