Classification of Liouville foliations of integrable topological billiards in magnetic fields

Author:

Vedyushkina Viktoriya Viktorovna1,Pustovoitov Sergey Evgen'evich1

Affiliation:

1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract

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.

Funder

Russian Science Foundation

Publisher

Steklov Mathematical Institute

Subject

Algebra and Number Theory

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