Realization of the numerical invariant of the Seifert fibration of integrable systems by billiards

DOI10.3103/S0027132220040075zbMath1468.37049OpenAlexW3138574640MaRDI QIDQ2027873

V. A. Kibkalo, V. V. Vedyushkina

Publication date: 28 May 2021

Published in: Moscow University Mathematics Bulletin (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s0027132220040075

zbMATH Keywords

integrabilityHamiltonian systembilliardFomenko-Zieschang invariantLiouville foliationSeifert foliation

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39) Dynamical systems with singularities (billiards, etc.) (37C83) Computational methods for invariant manifolds of dynamical systems (37M21)

Related Items (11)

Billiard ordered games and books ⋮ Liouville foliations of topological billiards with slipping ⋮ Topological classification of billiards bounded by confocal quadrics in three-dimensional Euclidean space ⋮ Realizing integrable Hamiltonian systems by means of billiard books ⋮ Modeling the degenerate singularities of integrable billiard systems by billiard books ⋮ Topology of isoenergy 5-surfaces of a three-axial ellipsoid with a Hooke potential ⋮ Local modeling of Liouville foliations by billiards: implementation of edge invariants ⋮ Billiards with changing geometry and their connection with the implementation of the Zhukovsky and Kovalevskaya cases ⋮ Billiards and integrable systems ⋮ Billiard with slipping at any rational angle ⋮ Topology of Liouville foliations of integrable billiards on table-complexes

Cites Work

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• Integrable billiards model important integrable cases of rigid body dynamics
• Billiards and integrability in geometry and physics. New scope and new potential
• A TOPOLOGICAL INVARIANT AND A CRITERION FOR THE EQUIVALENCE OF INTEGRABLE HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM
• A topological classification of billiards in locally planar domains bounded by arcs of confocal quadrics
• Billiard books model all three-dimensional bifurcations of integrable Hamiltonian systems
• The Fomenko-Zieschang invariants of nonconvex topological billiards

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