Geodesic
Degenerate billiards
Informatics and Automation, Modern problems of mechanics, Tome 295 (2016), pp. 53-71

Voir la notice de l'article provenant de la source Math-Net.Ru

In an ordinary billiard system, 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 $1$, we say that the billiard is degenerate. We study those trajectories of degenerate billiards that have an infinite number of collisions with the scatterer. Degenerate billiards appear as limits of systems with elastic reflections or as small-mass limits of systems with singularities in celestial mechanics. We prove the existence of trajectories of such systems that shadow the trajectories of the corresponding degenerate billiards. The proofs are based on a version of the method of an anti-integrable limit. 
@article{TRSPY_2016_295_a3,
     author = {S. V. Bolotin},
     title = {Degenerate billiards},
     journal = {Informatics and Automation},
     pages = {53--71},
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     volume = {295},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2016_295_a3/}
}
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S. V. Bolotin. Degenerate billiards. Informatics and Automation, Modern problems of mechanics, Tome 295 (2016), pp. 53-71. http://geodesic.mathdoc.fr/item/TRSPY_2016_295_a3/