16 citations · 38 across the 5 of their papers we have counts for
5 papers
Superintegrability of 3-dimensional Hamiltonian systems with conformally Euclidean metrics. Oscillator-related and Kepler-related systems
Jose F. Carinena, Manuel F. Ranada, Mariano Santander
We study four particular 3-dimensional natural Hamiltonian systems defined in conformally Euclidean spaces. We prove their superintegrability and we obtain, in the four cases, the…
Superintegrability on the 3-dimensional spaces with curvature. Oscillator-related and Kepler-related systems on the Sphere and on the Hyperbolic space
Jose F. Cariñena, Manuel F. Rañada, Mariano Santander
The superintegrability of several Hamiltonian systems defined on three-dimensional configuration spaces of constant curvature is studied. We first analyze the properties of the Kil…
Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem
Jose F. Cariñena, Manuel F. Rañada
The existence of quasi-bi-Hamiltonian structures for the Kepler problem is studied. We first relate the superintegrability of the system with the existence of two complex functions…
Geometry of Lie integrability by quadratures
J. F. Cariñena, F. Falceto, J. Grabowski +1
In this paper we extend the Lie theory of integration in two different ways. First we consider a finite dimensional Lie algebra of vector fields and discuss the most general condit…
Higher-order superintegrability of a Holt related potential
R. Campoamor-Stursberg, J. F. Cariñena, M. F. Rañada
In a recent paper, Post and Winternitz studied the properties of two-dimensional Euclidean potentials that are linear in one of the two Cartesian variables. In particular, they pro…