Superintegrable system on a sphere with the integral of higher degree

DOI10.1134/S156035470906001XzbMath1229.70052OpenAlexW2016075315MaRDI QIDQ653255

Alexander A. Kilin, Alexey V. Borisov, Ivan. S. Mamaev

Publication date: 9 January 2012

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s156035470906001x

zbMATH Keywords

superintegrable systemsHooke centersystems with a potential

Mathematics Subject Classification ID

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) (n)-body problems (70F10) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65)

Related Items (12)

Necessary conditions for classical super-integrability of a certain family of potentials in constant curvature spaces ⋮ An integrable Hénon–Heiles system on the sphere and the hyperbolic plane ⋮ The Tremblay-Turbiner-Winternitz system as extended Hamiltonian ⋮ Extended Hamiltonians and shift, ladder functions and operators ⋮ On algebraic construction of certain integrable and super-integrable systems ⋮ A multiple scales approach to maximal superintegrability ⋮ Remarks on integrable systems ⋮ Superintegrable generalizations of the Kepler and Hook problems ⋮ The spatial problem of 2 bodies on a sphere. Reduction and stochasticity ⋮ New superintegrable models on spaces of constant curvature ⋮ More on superintegrable models on spaces of constant curvature ⋮ Three and four-body systems in one dimension: integrability, superintegrability and discrete symmetries

Cites Work

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• Integrable systems on the sphere with elastic interaction potentials
• Superintegrable systems on a sphere
• Superintegrable three-body systems on the line
• Two-dimensional geodesic flows having first integrals of higher degree

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