Extensions of Hamiltonian systems dependent on a rational parameter

Abstract

The technique of "extension" allows to build $(n+1)$-dimensional Hamiltonian systems with a non-trivial polynomial in the momenta first integral of any given degree starting from a $n$-dimensional Hamiltonian satisfying some additional properties. Until now, the application of the method was restricted to integer values of a certain fundamental parameter determining the degree of the additional first integral. In this article we show how this technique can be generalized to any rational value of the same parameter. Several examples are given, among them the anisotropic oscillator and a special case of the Tremblay-Turbiner-Winternitz system.

References in corpus (4)

• Classical and Quantum Superintegrability with Applications
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• Tools for Verifying Classical and Quantum Superintegrability
• Superintegrable Extensions of Superintegrable Systems

Cited by in corpus (9)

• Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability
• The Tremblay-Turbiner-Winternitz system as extended Hamiltonian
• Extended Hamiltonians, Coupling-Constant Metamorphosis and the Post-Winternitz System
• On the Extended-Hamiltonian Structure of Certain Superintegrable Systems on Constant-Curvature Riemannian and Pseudo-Riemannian Surfaces
• Extended Hamiltonians and shift, ladder functions and operators
• Modified Laplace-Beltrami quantization of natural Hamiltonian systems with quadratic constants of motion
• Born-Jordan and Weyl Quantizations of the 2D Anisotropic Harmonic Oscillator
• More on superintegrable models on spaces of constant curvature
• Extensions of non-natural Hamiltonians