Topological invariants of some ordered billiard games

DOI10.3103/S0027132224700177MaRDI QIDQ6632305

K. E. Turina

Publication date: 4 November 2024

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

zbMATH Keywords

integrable Hamiltonian systembilliardFomenko-Zieschang invariantconfocal quadricsintegrable billiardisoenergy surfacebilliard bookordered billiard game

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)

Cites Work

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• The Liouville foliation of the billiard book modelling the Goryachev-Chaplygin case
• Billiard ordered games and books
• 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
• THE TOPOLOGY OF SURFACES OF CONSTANT ENERGY IN INTEGRABLE HAMILTONIAN SYSTEMS, AND OBSTRUCTIONS TO INTEGRABILITY
• Billiard books model all three-dimensional bifurcations of integrable Hamiltonian systems
• Billiard books realize all bases of Liouville foliations of integrable Hamiltonian systems

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