The Liouville foliation of the billiard book modelling the Goryachev-Chaplygin case

DOI10.3103/S0027132220010076zbMath1448.37067OpenAlexW3042866516MaRDI QIDQ785958

V. V. Vedyushkina

Publication date: 12 August 2020

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

Full work available at URL: https://doi.org/10.3103/s0027132220010076

zbMATH Keywords

Fomenko-Zieschang invariantGoryachev-Chaplygin integrable case

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Integrable cases of motion in rigid body dynamics (70E40) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

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Cites Work

• Reducing the degree of integrals of Hamiltonian systems by using billiards
• 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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