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. 
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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/

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