Geodesic
Billiards and nonholonomic distributions
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 56-64 
Y. Baryshnikov; V. Zharnitsky. Billiards and nonholonomic distributions. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 56-64. http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a5/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In this note, billiards with full families of periodic orbits are considered. It is shown that construction of a convex billiard with a “rational” caustic (i.e., carrying only periodic orbits) can be reformulated as a problem of finding a closed curve tangent to a $(N-1)$-dimensional distribution on a $(2N-1)$-dimensional manifold. The properties of this distribution are described as well as some important consequences for the billiards with rational caustics. A very particular application of our construction states that an ellipse can be infinitesimally perturbed so that any chosen rational elliptic caustic will persist.

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