The topology of Liouville foliations of three-dimensional billiards with slipping
https://doi.org/10.22405/2226-8383-2025-26-2-7-32
Abstract
Billiards in three-dimensional confocal domains with slipping along the boundary are considered. Such dynamical systems are Liouville integrable in piecewise-smooth sense. In twodimensional case, class of billiards with slipping was introduced by A.T.Fomenko. For several types of confocal billiards with slipping the classes of homeomorphism of constant energy surfaces are found, the bifurcation diagrams are constructed and the topology of Liouville foliation in small neighborhoods of singular and non-singular fibers is described.
About the Authors
Gleb Vladimirovich Belozerov
Lomonosov Moscow State University
Russian Federation
Russian Federation
Vladimir Nikolaevich Zavyalov
Lomonosov Moscow State University; Bauman Moscow State Technical University; Moscow Center for Fundamental and Applied Mathematics
Russian Federation
Russian Federation
postgraduate student
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Review
For citations:
Belozerov G.V., Zavyalov V.N. The topology of Liouville foliations of three-dimensional billiards with slipping. Chebyshevskii Sbornik. 2025;26(2):7-32. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-2-7-32
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