Billiards and integrability in geometry and physics. New scope and new potential

DOI10.3103/S0027132219030021zbMath1429.37030OpenAlexW2956278080MaRDI QIDQ2287140

A. T. Fomenko, V. V. Vedyushkina

Publication date: 23 January 2020

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

Full work available at URL: https://doi.org/10.3103/s0027132219030021

zbMATH Keywords

integrable systemsbifurcationssymmetries

Mathematics Subject Classification ID

Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical systems with singularities (billiards, etc.) (37C83)

Related Items (15)

Liouville foliations of topological billiards with slipping ⋮ Realizing integrable Hamiltonian systems by means of billiard books ⋮ Parabolicity of degenerate singularities in axisymmetric Euler systems with a gyrostat ⋮ Modeling the degenerate singularities of integrable billiard systems by billiard books ⋮ Conformal transformations and integrable mechanical billiards ⋮ An elliptic billiard in a potential force field: classification of motions, topological analysis ⋮ Topology of isoenergy 5-surfaces of a three-axial ellipsoid with a Hooke potential ⋮ Topological classification of integrable geodesic billiards on quadrics in three-dimensional Euclidean space ⋮ 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 ⋮ Realization of the numerical invariant of the Seifert fibration of integrable systems by billiards ⋮ 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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