Superintegrable deformations of superintegrable systems : Quadratic superintegrability and higher-order superintegrability

Abstract

The superintegrability of four Hamiltonians $\widetilde{H_r}=\lambda H_r$, $r=a,b,c,d$, where $H_r$ are known Hamiltonians and $\lambda$ is a certain function defined on the configuration space and depending of a parameter $\kappa$, is studied. The new Hamiltonians, and the associated constants of motion $J_{ri}$, $i=1,2,3$, are continous functions of the parameter $\kappa$. The first part is concerned with separability and quadratic superintegrability (the integrals of motion are quadratic in the momenta) and the second part is devoted to the existence of higher-order superintegrability. The results obtained in the second part are related with the TTW and the PW systems.

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Cited by in corpus (7)

• Quantum oscillator and Kepler-Coulomb problems in curved spaces: deformed shape invariance, point canonical transformations, and rational extensions
• Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability
• Superintegrable systems with a position dependent mass : Kepler-related and Oscillator-related systems
• Curvature as an integrable deformation
• Hydrogen Atom in Electric and Magnetic Fields: Dynamical Symmetries, Superintegrable and Integrable Systems, Exact Solutions
• Superintegrability of 3-dimensional Hamiltonian systems with conformally Euclidean metrics. Oscillator-related and Kepler-related systems
• Superintegrability on the 3-dimensional spaces with curvature. Oscillator-related and Kepler-related systems on the Sphere $S^3$ and on the Hyperbolic space $H^3$