Topological obstacles to the realizability of integrable Hamiltonian systems by billiards

DOI10.1134/S106456241905020XzbMath1439.37056OpenAlexW2986020317MaRDI QIDQ2304361

A. T. Fomenko, V. V. Vedyushkina

Publication date: 11 March 2020

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

Full work available at URL: https://doi.org/10.1134/s106456241905020x

zbMATH Keywords

integrable billiardsLiouville equivalence

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30) 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 (2)

Billiards and integrable systems ⋮ Saddle Singularities in Integrable Hamiltonian Systems: Examples and Algorithms

Cites Work

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• Integrable billiards model important integrable cases of rigid body dynamics
• Topological classification of integrable Hamiltonian systems in a potential field on surfaces of revolution
• A topological classification of billiards in locally planar domains bounded by arcs of confocal quadrics
• Integrable topological billiards and equivalent dynamical systems
• Billiard books model all three-dimensional bifurcations of integrable Hamiltonian systems
• Polynomial non-integrability of magnetic billiards on the sphere and the hyperbolic plane
• The Fomenko-Zieschang invariants of nonconvex topological billiards

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