Geodesic
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/}
}
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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/