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.

10 pages

References in corpus (5)

• Superintegrable 3-body systems on the line
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• The Tremblay-Turbiner-Winternitz system on spherical and hyperbolic spaces : Superintegrability, curvature-dependent formalism and complex factorization
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Cited by in corpus (2)

• Extended Hamiltonians and shift, ladder functions and operators
• Doubly Exotic $N$th-order Order Superintegrable Classical Systems Separating in Cartesian Coordinates