Geodesic
Classification of Liouville foliations of integrable topological billiards in magnetic fields
Sbornik. Mathematics, Tome 214 (2023) no. 2, pp. 166-196

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The topology of the Liouville foliations of integrable magnetic topological billiards, systems in which a ball moves on piecewise smooth two-dimensional surfaces in a constant magnetic field, is considered. The Fomenko-Zieschang invariants of Liouville equivalence are calculated for the Hamiltonian systems arising, and the topology of invariant 3-manifolds, isointegral and isoenergy ones, is investigated. The Liouville equivalence of such billiards to some known Hamiltonian systems is discovered, for instance, to the geodesic flows on 2-surfaces and to systems of rigid body dynamics. In particular, peculiar saddle singularities are discovered in which singular circles have different orientations — such systems were also previously encountered in mechanical systems in a magnetic field on surfaces of revolution homeomorphic to a 2-sphere. Bibliography: 13 titles.
Keywords: integrable systems, magnetic field, topological billiard
Mots-clés : Liouville foliation, Fomenko-Zieschang invariant. 
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     author = {V. V. Vedyushkina and S. E. Pustovoitov},
     title = {Classification of {Liouville} foliations of integrable topological billiards in magnetic fields},
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V. V. Vedyushkina; S. E. Pustovoitov. Classification of Liouville foliations of integrable topological billiards in magnetic fields. Sbornik. Mathematics, Tome 214 (2023) no. 2, pp. 166-196. http://geodesic.mathdoc.fr/item/SM_2023_214_2_a1/