The Tremblay-Turbiner-Winternitz system as extended Hamiltonian

Abstract

We generalize the idea of "extension of Hamiltonian systems" -- developed in a series of previous articles -- which allows the explicit construction of Hamiltonian systems with additional non-trivial polynomial first integrals of arbitrarily high degree, as well as the determination of new superintegrable systems from old ones. The present generalization, that we call "modified extension of Hamiltonian systems", produces the third independent first integral for the (complete) Tremblay-Turbiner-Winternitz (TTW) system, as well as for the caged anisotropic oscillator in dimension two.

arXiv comment10 pages

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Cited by in corpus (9)

• On the Extended-Hamiltonian Structure of Certain Superintegrable Systems on Constant-Curvature Riemannian and Pseudo-Riemannian Surfaces
• Extended Hamiltonians, Coupling-Constant Metamorphosis and the Post-Winternitz System
• Extended Hamiltonians and shift, ladder functions and operators
• Modified Laplace-Beltrami quantization of natural Hamiltonian systems with quadratic constants of motion
• Superintegrability and Deformed Oscillator Realizations of Quantum TTW Hamiltonians on Constant-Curvature Manifolds and with Reflections in a Plane
• Doubly Exotic $N$th-order Order Superintegrable Classical Systems Separating in Cartesian Coordinates
• Separation of Variables and Superintegrability on Riemannian Coverings
• Born-Jordan and Weyl Quantizations of the 2D Anisotropic Harmonic Oscillator
• Extensions of non-natural Hamiltonians