Realization of geodesic flows with a linear first integral by billiards with slipping
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Published:2022
Issue:12
Volume:213
Page:1645-1664
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ISSN:1064-5616
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Container-title:Sbornik: Mathematics
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language:en
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Short-container-title:Sb. Math.
Author:
Vedyushkina Viktoriya Viktorovna1,
Zav'yalov Vladimir Nikolaevich1
Affiliation:
1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
Abstract
An arbitrary geodesic flow on the projective plane or Klein bottle with an additional, linear in the momentum, first integral is modelled using billiards with slipping on table complexes. The requisite table of a circular topological billiard with slipping is constructed algorithmically. Furthermore, linear integrals of geodesic flows can be reduced to the same canonical integral of a circular planar billiard.
Bibliography: 36 titles.
Funder
Russian Science Foundation
Publisher
Steklov Mathematical Institute
Subject
Algebra and Number Theory
Reference63 articles.
1. Integrable Hamiltonian Systems
2. Topological obstructions to the integrability of natural mechanical systems;V. V. Kozlov;Dokl. Akad. Nauk SSSR,1979
Cited by
2 articles.
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