A new approach to the higher-order superintegrability of the Tremblay-Turbiner-Winternitz system

Abstract

The higher-order superintegrability of systems separable in polar coordinates is studied using an approch that was previously applied for the study of the superintegrability of a generalized Smorodinsky-Winternitz system. The idea is that the additional constant of motion can be factorized as the product of powers of two particular rather simple complex functions (here denoted by $M$ and $N$). This technique leads to a proof of the superintegrability of the Tremblay-Turbiner-Winternitz system and to the explicit expression of the constants of motion. A second family (related with the first one) of superintegrable systems is also studied.

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Cited by in corpus (13)

• The Tremblay-Turbiner-Winternitz system on spherical and hyperbolic spaces : Superintegrability, curvature-dependent formalism and complex factorization
• Superintegrable systems with a position dependent mass : Kepler-related and Oscillator-related systems
• Superintegrable systems on spaces of constant curvature
• Symmetries in superintegrable deformations of oscillator/Coulomb systems: "holomorphic factorization"
• Higher-order superintegrability of a Holt related potential
• Superintegrable deformations of superintegrable systems : Quadratic superintegrability and higher-order superintegrability
• Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem
• A family of fourth-order superintegable systems with rational potentials related to Painlevé VI
• Jacobi last multiplier and two-dimensional superintegrable oscillators
• Noncompact ${\mathbf{CP}}^N$ as a phase space of superintegrable systems
• Superintegrability of the Post-Winternitz system on spherical and hyperbolic spaces
• Extensions of natural Hamiltonians
• Superintegrable deformations of oscillator and Coulomb systems