Geodesic
Billiards and nonholonomic distributions
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 56-64

Voir la notice de l'article 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. 
@article{ZNSL_2003_300_a5,
     author = {Y. Baryshnikov and V. Zharnitsky},
     title = {Billiards and nonholonomic distributions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {56--64},
     publisher = {mathdoc},
     volume = {300},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a5/}
}
TY  - JOUR
AU  - Y. Baryshnikov
AU  - V. Zharnitsky
TI  - Billiards and nonholonomic distributions
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2003
SP  - 56
EP  - 64
VL  - 300
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a5/
LA  - en
ID  - ZNSL_2003_300_a5
ER  - 
%0 Journal Article
%A Y. Baryshnikov
%A V. Zharnitsky
%T Billiards and nonholonomic distributions
%J Zapiski Nauchnykh Seminarov POMI
%D 2003
%P 56-64
%V 300
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a5/
%G en
%F ZNSL_2003_300_a5
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/