Superintegrability on the 3-dimensional spaces with curvature. Oscillator-related and Kepler-related systems on the Sphere $S^3$ and on the Hyperbolic space $H^3$

Cariñena, J.F. (Universidad de Zaragoza) ; Rañada, M.F. (Universidad de Zaragoza) ; Santander M.

Resumen: 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.

Idioma: Inglés

DOI: 10.1088/1751-8121/ac17a4

Año: 2021

Publicado en: Journal of Physics A-Mathematical and Theoretical 54, 36 (2021), 365201 [27 pp.]
ISSN: 1751-8113

Factor impacto JCR: 2.331 (2021)

Categ. JCR: PHYSICS, MATHEMATICAL rank: 14 / 56 = 0.25 (2021) - Q1 - T1
Categ. JCR: PHYSICS, MULTIDISCIPLINARY rank: 45 / 86 = 0.523 (2021) - Q3 - T2

Factor impacto CITESCORE: 4.0 - Mathematics (Q1) - Physics and Astronomy (Q2)

Factor impacto SCIMAGO: 0.76 - Mathematical Physics (Q1) - Statistics and Probability (Q1) - Statistical and Nonlinear Physics (Q1) - Physics and Astronomy (miscellaneous) (Q1)

Tipo y forma: Article (PrePrint)

Área (Departamento): Área Física Teórica (Dpto. Física Teórica)