Ángel Ballesteros, Alberto Enciso, Francisco J. Herranz, Orlando Ragnisco, Danilo Riglioni, “Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform”, SIGMA, 7 (2011), 048, 15 pp.

Instituto de Ciencias Matemáticas (CSIC-UAM-UCM-UC3M), Consejo Superior de Investigaciones Cientícas, C/ Nicolás Cabrera 14-16, E-28049 Madrid, Spain Dipartimento di Fisica, Università di Roma Tre and Istituto Nazionale di Fisica Nucleare sezione di Roma Tre, Via Vasca Navale 84, I-00146 Roma, Italy The Stäckel transform is applied to the geodesic motion on Euclidean space, through the harmonic oscillator and Kepler–Coloumb potentials, in order to obtain maximally superintegrable classical systems on -dimensional Riemannian spaces of nonconstant curvature. By one hand, the harmonic oscillator potential leads to two families of superintegrable systems which are interpreted as an intrinsic Kepler–Coloumb system on a hyperbolic curved space and as the so-called Darboux III oscillator. On the other, the Kepler–Coloumb potential gives rise to an oscillator system on a spherical curved space as well as to the Taub-NUT oscillator. Their integrals of motion are explicitly given. The role of the (flat/curved) Fradkin tensor and Laplace–Runge–Lenz -vector for all of these Hamiltonians is highlighted throughout the paper. The corresponding quantum maximally superintegrable systems are also presented. coupling constant metamorphosis, integrable systems, curvature, harmonic oscillator, Kepler–Coulomb, Fradkin tensor, Laplace–Runge–Lenz vector, Taub-NUT, Darboux surfaces Ángel Ballesteros, Alberto Enciso, Francisco J. Herranz, Orlando Ragnisco, Danilo Riglioni, “Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform”, Bibitem{BalEncHer11} by 'Angel~Ballesteros, Alberto Enciso, Francisco J.~Herranz, Orlando Ragnisco, Danilo Riglioni paper Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the St'ackel Transform jour SIGMA yr 2011 vol 7 papernumber 048 totalpages 15 mathnet{http://mi.mathnet.ru/sigma606} crossref{http://dx.doi.org/10.3842/SIGMA.2011.048} mathscinet{http://www.ams.org/mathscinet-getitem?mr=2804588} isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000290556600001} scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84855223715} Panahi H., Alizadeh Z., “Deformed Oscillator Algebra for Quantum Superintegrable Systems in Two-Dimensional Euclidean Space and on a Complex Two-Sphere”, Ballesteros A., Enciso A., Herranz F.J., Ragnisco O., Riglioni D., “An Exactly Solvable Deformation of the Coulomb Problem Associated With the Taub-Nut Metric”, Latini D., Ragnisco O., “the Classical Taub-Nut System: Factorization, Spectrum Generating Algebra and Solution To the Equations of Motion”, Ranada M.F., “Superintegrable Deformations of Superintegrable Systems: Quadratic Superintegrability and Higher-Order Superintegrability”, Yuxuan Chen, Ernie G. Kalnins, Qiushi Li, Willard Miller Jr., “Examples of Complete Solvability of 2D Classical Superintegrable Systems”, Source.


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