Liouville foliations of topological billiards with slipping

DOI10.1134/S1061920821010052zbMath1469.37045OpenAlexW3138132970MaRDI QIDQ829070

A. T. Fomenko, V. V. Vedyushkina, V. N. Zav'yalov

Publication date: 5 May 2021

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1061920821010052

zbMATH Keywords

integrable billiardsLiouville foliationsbilliards with slipping

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 (4)

Billiard ordered games and books ⋮ Topological classification of billiards bounded by confocal quadrics in three-dimensional Euclidean space ⋮ Topology of isoenergy 5-surfaces of a three-axial ellipsoid with a Hooke potential ⋮ Billiards with changing geometry and their connection with the implementation of the Zhukovsky and Kovalevskaya cases

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Integrable billiards model important integrable cases of rigid body dynamics
• The topology of the analog of Kovalevskaya integrability case on the Lie algebra \(\mathrm{so}(4)\) under zero area integral
• An integrable deformation of an ellipse of small eccentricity is an ellipse
• Angular billiard and algebraic Birkhoff conjecture
• Topological analysis of the Liouville foliation for the Kovalevskaya integrable case on the Lie algebra \(\operatorname{so}(4)\)
• Modeling nondegenerate bifurcations of closures of solutions for integrable systems with two degrees of freedom by integrable topological billiards
• The Liouville foliation of the billiard book modelling the Goryachev-Chaplygin case
• Integrable Birkhoff billiards
• Topological classification of integrable geodesic flows on orientable two-dimensional Riemannian manifolds with additional integral depending on momenta linearly or quadratically
• On the local Birkhoff conjecture for convex billiards
• The Liouville foliation of nonconvex topological billiards
• On complex structures on two-dimensional tori admitting metrics with nontrivial quadratic integral
• Topological classification of Liouville foliations for the Kovalevskaya integrable case on the Lie algebra \(\operatorname{so}(3, 1)\)
• On two-dimensional polynomially integrable billiards on surfaces of constant curvature
• Realization of the numerical invariant of the Seifert fibration of integrable systems by billiards
• Topological modeling of integrable systems by billiards: realization of numerical invariants
• 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
• Liouville integrable generalized billiard flows and Poncelet type theorems
• A TOPOLOGICAL INVARIANT AND A CRITERION FOR THE EQUIVALENCE OF INTEGRABLE HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM
• GEODESIC FLOWS ON TWO-DIMENSIONAL MANIFOLDS WITH AN ADDITIONAL FIRST INTEGRAL THAT IS POLYNOMIAL IN THE VELOCITIES
• A topological classification of billiards in locally planar domains bounded by arcs of confocal quadrics
• The symplectic topology of completely integrable Hamiltonian systems
• ON TYPICAL TOPOLOGICAL PROPERTIES OF INTEGRABLE HAMILTONIAN SYSTEMS
• CLASSIFICATION OF GEODESIC FLOWS OF LIOUVILLE METRICS ON THE TWO-DIMENSIONAL TORUS UP TO TOPOLOGICAL EQUIVALENCE
• Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry
• The method of loop molecules and the topology of the Kovalevskaya top
• Integrable topological billiards and equivalent dynamical systems
• Billiard books model all three-dimensional bifurcations of integrable Hamiltonian systems
• Topology of Liouville foliations in the Steklov and the Sokolov integrable cases of Kirchhoff's equations
• Topological classification of quadratic-integrable geodesic flows on a two-dimensional torus
• Topological classification of Liouville foliations for the Kovalevskaya integrable case on the Lie algebra so(4)
• Saddle Singularities in Integrable Hamiltonian Systems: Examples and Algorithms
• Integrable billiard systems realize toric foliations on lens spaces and the 3-torus
• Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards
• Polynomial non-integrability of magnetic billiards on the sphere and the hyperbolic plane
• The Fomenko-Zieschang invariants of nonconvex topological billiards

This page was built for publication: Liouville foliations of topological billiards with slipping