Factorization approach to superintegrable systems: Formalism and applications

Abstract

The factorization technique for superintegrable Hamiltonian systems is revisited and applied in order to obtain additional (higher-order) constants of the motion. In particular, the factorization approach to the classical anisotropic oscillator on the Euclidean plane is reviewed, and new classical (super)integrable anisotropic oscillators on the sphere are constructed. The Tremblay-Turbiner-Winternitz system on the Euclidean plane is also studied from this viewpoint.

15 pages, 3 figures. Minor corrections. Based on the contribution presented at "The IX International Symposium on Quantum Theory and Symmetries" (QTS-9), July 13-18, 2015, Yerevan, Armenia

References in corpus (9)

• Reduction of superintegrable systems: the anisotropic harmonic oscillator
• Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability
• Superintegrability of the Caged Anisotropic Oscillator
• Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles
• Factorizations of one dimensional classical systems
• Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems
• An exactly solvable deformation of the Coulomb problem associated with the Taub-NUT metric
• A new integrable anisotropic oscillator on the two-dimensional sphere and the hyperbolic plane
• The classical Taub-Nut System: factorization, spectrum generating algebra and solution to the equations of motion

Cited by in corpus (5)

• The anisotropic oscillator on curved spaces: A new exactly solvable model
• The Perlick system type I: from the algebra of symmetries to the geometry of the trajectories
• Extended Hamiltonians and shift, ladder functions and operators
• Quantum, classical symmetries and action-angle variables by factorization of superintegrable systems
• Curvature as an integrable deformation