Topological modeling of integrable systems by billiards: realization of numerical invariants

DOI10.1134/S1064562420040201zbMath1494.37039OpenAlexW3158737933MaRDI QIDQ2243763

V. V. Vedyushkina, A. T. Fomenko, V. A. Kibkalo

Publication date: 11 November 2021

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562420040201

zbMATH Keywords

integrabilityHamiltonian systembilliardFomenko-Zieschang invariantCW complex

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)

Related Items (9)

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 ⋮ 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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• An integrable deformation of an ellipse of small eccentricity is an ellipse
• Angular billiard and algebraic Birkhoff conjecture
• On the local Birkhoff conjecture for convex billiards
• On two-dimensional polynomially integrable billiards on surfaces of constant curvature
• Billiards and integrability in geometry and physics. New scope and new potential
• Implementation of integrable systems by topological, geodesic billiards with potential and magnetic field
• Algebraic Birkhoff conjecture for billiards on sphere and hyperbolic plane
• Algebraic non-integrability of magnetic billiards
• Billiard books model all three-dimensional bifurcations of integrable Hamiltonian systems
• Billiards bounded by arcs of confocal quadrics on the Minkowski plane
• Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards
• Polynomial non-integrability of magnetic billiards on the sphere and the hyperbolic plane

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