Geodesic
Topological analysis of a~billiard in elliptic ring in a~potential field
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 6, pp. 201-225

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

We study a billiard in a domain bounded by two confocal ellipses. The Hooke potential is placed at the center of the ellipses. This dynamic system turns out to be Liouville integrable. Therefore, we can make a topological analysis studying the foliation of the phase manifold by integrals. We calculate Fomenko–Zieschang invariants (marked molecules) for isoenergy manifolds of every level of the Hamiltonian, and also give examples of other integrable systems that are Liouville equivalent to our billiard system. 
@article{FPM_2019_22_6_a8,
     author = {S. E. Pustovoytov},
     title = {Topological analysis of a~billiard in elliptic ring in a~potential field},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {201--225},
     publisher = {mathdoc},
     volume = {22},
     number = {6},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2019_22_6_a8/}
}
TY  - JOUR
AU  - S. E. Pustovoytov
TI  - Topological analysis of a~billiard in elliptic ring in a~potential field
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2019
SP  - 201
EP  - 225
VL  - 22
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2019_22_6_a8/
LA  - ru
ID  - FPM_2019_22_6_a8
ER  - 
%0 Journal Article
%A S. E. Pustovoytov
%T Topological analysis of a~billiard in elliptic ring in a~potential field
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2019
%P 201-225
%V 22
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2019_22_6_a8/
%G ru
%F FPM_2019_22_6_a8
S. E. Pustovoytov. Topological analysis of a~billiard in elliptic ring in a~potential field. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 6, pp. 201-225. http://geodesic.mathdoc.fr/item/FPM_2019_22_6_a8/