An elliptic billiard in a potential force field: classification of motions, topological analysis

DOI10.1070/SM9296zbMath1448.37066OpenAlexW3012202544MaRDI QIDQ5122441

I. F. Kobtsev

Publication date: 22 September 2020

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

Full work available at URL: https://doi.org/10.1070/sm9296

zbMATH Keywords

potentialbifurcationsintegrable Hamiltonian systemLiouville foliationbilliard in ellipse

Mathematics Subject Classification ID

Bifurcations of singular points in dynamical systems (37G10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Integrable cases of motion in rigid body dynamics (70E40) Dynamical systems with singularities (billiards, etc.) (37C83)

Related Items (9)

Topological analysis of an elliptic billiard in a fourth-order potential field ⋮ Topological classification of billiards bounded by confocal quadrics in three-dimensional Euclidean space ⋮ Realizing integrable Hamiltonian systems by means of billiard books ⋮ Classification of singularities of the Liouville foliation of an integrable elliptical Billiard with a potential of fourth degree ⋮ Conformal transformations and integrable mechanical billiards ⋮ Topology of isoenergy 5-surfaces of a three-axial ellipsoid with a Hooke potential ⋮ Force evolutionary billiards and billiard equivalence of the Euler and Lagrange cases ⋮ Topological analysis of a billiard bounded by confocal quadrics in a potential field ⋮ Saddle Singularities in Integrable Hamiltonian Systems: Examples and Algorithms

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