Billiard books model all three-dimensional bifurcations of integrable Hamiltonian systems

DOI10.1070/SM9039zbMath1408.37098OpenAlexW2893224023WikidataQ129202160 ScholiaQ129202160MaRDI QIDQ4624849

Irina S. Kharcheva, V. V. Vedyushkina

Publication date: 19 February 2019

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

Full work available at URL: https://doi.org/10.1070/sm9039

zbMATH Keywords

integrable systembilliardFomenko-Zieschang invariantLiouville equivalence

Mathematics Subject Classification ID

Related Items (22)

Billiard ordered games and books ⋮ Liouville foliations of topological billiards with slipping ⋮ Topological classification of billiards bounded by confocal quadrics in three-dimensional Euclidean space ⋮ Realizing integrable Hamiltonian systems by means of billiard books ⋮ Modeling the degenerate singularities of integrable billiard systems by billiard books ⋮ Integrable billiard systems realize toric foliations on lens spaces and the 3-torus ⋮ Topology of isoenergy 5-surfaces of a three-axial ellipsoid with a Hooke potential ⋮ Local modeling of Liouville foliations by billiards: implementation of edge invariants ⋮ 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 ⋮ Force evolutionary billiards and billiard equivalence of the Euler and Lagrange cases ⋮ Billiard books realize all bases of Liouville foliations of integrable Hamiltonian systems ⋮ Isoenergetic manifolds of integrable billiard books ⋮ Realization of the numerical invariant of the Seifert fibration of integrable systems by billiards ⋮ Billiards and integrability in geometry and physics. New scope and new potential ⋮ Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards ⋮ Topological obstacles to the realizability of integrable Hamiltonian systems by billiards ⋮ Singularities of integrable Liouville systems, reduction of integrals to lower degree and topological billiards: Recent results ⋮ The Liouville foliation of the billiard book modelling the Goryachev-Chaplygin case ⋮ Implementation of integrable systems by topological, geodesic billiards with potential and magnetic field ⋮ Topology of Liouville foliations of integrable billiards on table-complexes ⋮ Saddle Singularities in Integrable Hamiltonian Systems: Examples and Algorithms

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