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JOURNALS // Chebyshevskii Sbornik // Archive

Chebyshevskii Sb., 2021 Volume 22, Issue 5, Pages 44–57 (Mi cheb1119)

This article is cited in 3 papers

Realization of focal singularities of integrable systems using billiard books with a Hooke potential field

V. V. Vedyushkinaa, V. A. Kibkaloab, S. E. Pustovoitova

a Lomonosov Moscow State University (Moscow)
b Moscow Center for Fundamental and Applied Mathematics (Moscow)

Abstract: 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.

UDC: 517.938.5

Received: 12.09.2021
Accepted: 21.12.2021

DOI: 10.22405/2226-8383-2021-22-5-44-57



© Steklov Math. Inst. of RAS, 2024