Realization of focal singularities of integrable systems using billiard books with a Hooke potential field
https://doi.org/10.22405/2226-8383-2021-22-5-44-57
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.
About the Authors
Victoria Viktorovna Vedyushkina
Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physics and mathematics
Vladislav Alexandrovich Kibkalo
Lomonosov Moscow State University; Moscow Center for Fundamental and Applied Mathematics
Russian Federation
Russian Federation
candidate of physics and mathematics
Sergey Evgenievich Pustovoitov
Lomonosov Moscow State University
Russian Federation
Russian Federation
postgraduate student
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Review
For citations:
Vedyushkina V.V., Kibkalo V.A., Pustovoitov S.E. Realization of focal singularities of integrable systems using billiard books with a Hooke potential field. Chebyshevskii Sbornik. 2021;22(5):44-57. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-5-44-57
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