Dynamical symmetries, bi-Hamiltonian structures, and superintegrable n=2 systems

DOI10.1063/1.533230zbMath1045.37034OpenAlexW2132968790MaRDI QIDQ2737922

Manuel F. Rañada

Publication date: 30 August 2001

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

Full work available at URL: https://doi.org/10.1063/1.533230

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) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

Related Items (9)

Superintegrable quantum u(3) systems and higher rank factorizations ⋮ Quasi-bi-Hamiltonian structures, complex functions and superintegrability: the Tremblay–Turbiner–Winternitz (TTW) and the Post–Winternitz (PW) systems ⋮ Quasi-bi-Hamiltonian structures of the 2-dimensional Kepler problem ⋮ Supersymmetry versus integrability in two-dimensional classical mechanics. ⋮ A summary on symmetries and conserved quantities of autonomous Hamiltonian systems ⋮ The harmonic oscillator on Riemannian and Lorentzian configuration spaces of constant curvature ⋮ Quasi-bi-Hamiltonian structures and superintegrability: study of a Kepler-related family of systems endowed with generalized Runge-Lenz integrals of motion ⋮ SYMPLECTIC STRUCTURES AND HAMILTONIAN FUNCTIONS CORRESPONDING TO A SYSTEM OF ODES ⋮ Lagrangian formalism for nonlinear second-order Riccati systems: One-dimensional integrability and two-dimensional superintegrability

Cites Work

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• Superintegrability of the Calogero–Moser system: Constants of motion, master symmetries, and time-dependent symmetries
• On the superintegrability of Calogero-Moser-Sutherland model
• Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions

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