Realization of focal singularities of integrable systems using billiard books with a Hooke potential field
Čebyševskij sbornik, Tome 22 (2021) no. 5, pp. 44-57
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Systems of particle motion in the Hooke central potential field on a billiard book glued from flat circular billiard domains are considered. An important class of nondegenerate focal singularities of the rank 0 of integrable systems with 2 degrees of freedom is completely realized by this class of billiards. Namely, for each semi-local focal singularity the constructed billiard system has a singularity fiberwise homeomorphic to the given one.
Keywords:
integrable billiard, focal singularity, Liouville foliation.
@article{CHEB_2021_22_5_a4,
author = {V. V. Vedyushkina and V. A. Kibkalo and S. E. Pustovoitov},
title = {Realization of focal singularities of integrable systems using billiard books with a {Hooke} potential field},
journal = {\v{C}eby\v{s}evskij sbornik},
pages = {44--57},
publisher = {mathdoc},
volume = {22},
number = {5},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/CHEB_2021_22_5_a4/}
}
TY - JOUR AU - V. V. Vedyushkina AU - V. A. Kibkalo AU - S. E. Pustovoitov TI - Realization of focal singularities of integrable systems using billiard books with a Hooke potential field JO - Čebyševskij sbornik PY - 2021 SP - 44 EP - 57 VL - 22 IS - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CHEB_2021_22_5_a4/ LA - ru ID - CHEB_2021_22_5_a4 ER -
%0 Journal Article %A V. V. Vedyushkina %A V. A. Kibkalo %A S. E. Pustovoitov %T Realization of focal singularities of integrable systems using billiard books with a Hooke potential field %J Čebyševskij sbornik %D 2021 %P 44-57 %V 22 %N 5 %I mathdoc %U http://geodesic.mathdoc.fr/item/CHEB_2021_22_5_a4/ %G ru %F CHEB_2021_22_5_a4
V. V. Vedyushkina; V. A. Kibkalo; S. E. Pustovoitov. Realization of focal singularities of integrable systems using billiard books with a Hooke potential field. Čebyševskij sbornik, Tome 22 (2021) no. 5, pp. 44-57. http://geodesic.mathdoc.fr/item/CHEB_2021_22_5_a4/