Billiards bounded by arcs of confocal quadrics on the Minkowski plane

DOI10.1070/SM9109zbMath1443.37042OpenAlexW2945838568MaRDI QIDQ5112422

E. E. Karginova

Publication date: 29 May 2020

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

Full work available at URL: https://doi.org/10.1070/sm9109

zbMATH Keywords

integrable systemMinkowski planebilliardFomenko-Zieschang invariantLiouville equivalence

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 (5)

Topological classification of billiards bounded by confocal quadrics in three-dimensional Euclidean space ⋮ Topology of integrable billiard in an ellipse in the Minkowski plane with the Hooke potential ⋮ Billiards with changing geometry and their connection with the implementation of the Zhukovsky and Kovalevskaya cases ⋮ Topological modeling of integrable systems by billiards: realization of numerical invariants ⋮ Billiards and integrability in geometry and physics. New scope and new potential

Cites Work

• Integrable billiards model important integrable cases of rigid body dynamics
• New approach to symmetries and singularities in integrable Hamiltonian systems
• The Chaplygin case in dynamics of a rigid body in fluid is orbitally equivalent to the Euler case in rigid body dynamics and to the Jacobi problem about geodesics on the ellipsoid
• Bifurcations of Liouville tori in elliptical billiards
• Morse-type theory for integrable Hamiltonian systems with tame integrals
• Topological invariants for elliptical billiards and geodesics on ellipsoids in the Minkowski space
• Symmetries groups of nice Morse functions on surfaces
• Algebra and Geometry Through Hamiltonian Systems
• Billiard Systems as the Models for the Rigid Body Dynamics
• Poncelet Porisms and Beyond
• 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 symplectic topology of completely integrable Hamiltonian systems
• Maximally symmetric cell decompositions of surfaces and their coverings
• A BORDISM THEORY FOR INTEGRABLE NONDEGENERATE HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM. A NEW TOPOLOGICAL INVARIANT OF HIGHER-DIMENSIONAL INTEGRABLE SYSTEMS
• Integrable topological billiards and equivalent dynamical systems
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