109652 20230519145523.0 doi 10.1088/1751-8121/ac17a4 sideral 127487 ART-2021-127487 eng Cariñena, J.F. Universidad de Zaragoza (orcid)0000-0003-4480-6535 Superintegrability on the 3-dimensional spaces with curvature. Oscillator-related and Kepler-related systems on the Sphere $S^3$ and on the Hyperbolic space $H^3$ 2021 Access copy available to the general public Unrestricted The superintegrability of several Hamiltonian systems defined on three-dimensional configuration spaces of constant curvature is studied. We first analyze the properties of the Killing vector fields, Noether symmetries and Noether momenta. Then we study the superintegrability of the harmonic oscillator, the Smorodinsky-Winternitz system and the harmonic oscillator with ratio of frequencies 1:1:2 and additional nonlinear terms on the three-dimensional sphere S-3 (kappa > 0) and on the hyperbolic space H-3 (kappa < 0). In the second part we present a study first of the Kepler problem and then of the Kepler problem with additional nonlinear terms in these two curved spaces, S-3 (kappa > 0) and H-3 (kappa < 0). We prove their superintegrability and we obtain, in all the cases, the maximal number of functionally independent integrals of motion. All the mathematical expressions are presented using the curvature kappa as a parameter, in such a way that particularizing for kappa > 0, kappa = 0, or kappa < 0, the corresponding properties are obtained for the system on the sphere S-3, the Euclidean space E-3, or the hyperbolic space H-3, respectively. info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 2.331 2021 PHYSICS, MATHEMATICAL 14 / 56 = 0.25 2021 Q1 T1 PHYSICS, MULTIDISCIPLINARY 45 / 86 = 0.523 2021 Q3 T2 0.76 2021 Mathematical Physics 2021 Q1 Statistics and Probability 2021 Q1 Statistical and Nonlinear Physics 2021 Q1 Physics and Astronomy (miscellaneous) 2021 Q1 4.0 2021 info:eu-repo/semantics/article info:eu-repo/semantics/submittedVersion Rañada, M.F. Universidad de Zaragoza (orcid)0000-0002-8402-2332 Santander M. 2004 405 Universidad de Zaragoza Dpto. Física Teórica Área Física Teórica 54, 36 (2021), 365201 [27 pp.] Journal of Physics A-Mathematical and Theoretical Journal of Physics A-Mathematical and Theoretical 1751-8113 461625 http://zaguan.unizar.es/record/109652/files/texto_completo.pdf Preprint 1523039 http://zaguan.unizar.es/record/109652/files/texto_completo.jpg?subformat=icon icon Preprint oai:zaguan.unizar.es:109652 articulos driver 2023-05-18-15:24:07 ARTICLE