127 citations · 1.2k across the 40 of their papers we have counts for
37 papers · 1 filter
Jacobi multipliers and Hojman symmetry
José F. Cariñena, Manuel F. Rañada
The geometric intrinsic approach to Hojman symmetry is developed and use is made of the theory of the Jacobi last multipliers to find the corresponding conserved quantity for non d…
Complex functions and geometric structures associated to the superintegrable Kepler-related family of systems endowed with generalized Runge-Lenz integrals of motion
Manuel F. Rañada
The existence of quasi-bi-Hamiltonian structures for a two-dimensional superintegrable -dependent Kepler-related problem is studied. We make use of an approach that…
Quantization of Hamiltonian systems with a position dependent mass: Killing vector fields and Noether momenta approach
José F. Cariñena, Manuel F. Rañada, Mariano Santander
The quantization of systems with a position dependent mass (PDM) is studied. We present a method that starts with the study of the existence of Killing vector fields for the PDM ge…
Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability
Jose F. Cariñena, Francisco J. Herranz, Manuel F. Rañada
The Eisenhart geometric formalism, which transforms an Euclidean natural Hamiltonian into a geodesic Hamiltonian with one additional degree of freedom, is applie…
Revisiting Lie integrability by quadratures from a geometric perspective
José F. Cariñena, Fernando Falceto, Janusz Grabowski +1
After a short review of the classical Lie theorem, a finite dimensional Lie algebra of vector fields is considered and the most general conditions under which the integral curves o…
Superintegrable systems with a position dependent mass : Kepler-related and Oscillator-related systems
Manuel F. Rañada
The superintegrability of two-dimensional Hamiltonians with a position dependent mass (pdm) is studied (the kinetic term contains a factor that depends of the radial coordinate…
A new look at the Feynman `hodograph' approach to the Kepler first law
Jose F. Cariñena, M. F. Rañada, M. Santander
Hodographs for the Kepler problem are circles. This fact, known since almost two centuries ago, still provides the simplest path to derive the Kepler first law. Through Feynman `lo…
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…
Geometrical and Dynamical Aspects of Nonlinear Higher-Order Riccati Systems
José F. Cariñena, Partha Guha, Manuel F. Rañada
We study a geometrical formulation of the nonlinear second-order Riccati equation (SORE) in terms of the projective vector field equation on , whichn in turn is related to the…
Jacobi multipliers, non-local symmetries and nonlinear oscillators
J. F. Cariñena, J. de Lucas, M. F. Rañada
Constants of motion, Lagrangians and Hamiltonians admitted by a family of relevant nonlinear oscillators are derived using a geometric formalism. The theory of the Jacobi last mult…
Superintegrable deformations of superintegrable systems : Quadratic superintegrability and higher-order superintegrability
Manuel F. Ranada
The superintegrability of four Hamiltonians , , where are known Hamiltonians and is a certain function defined on the configuration spac…
Superintegrability of the Post-Winternitz system on spherical and hyperbolic spaces
Manuel F. Ranada
The properties of the Tremblay-Turbiner-Winternitz system (related to the harmonic oscillator) were recently studied on the two-dimensional spherical () and hiperbolic…
A Quantum Quasi-Harmonic Nonlinear Oscillator with an Isotonic Term
Manuel F. Rañada
The properties of a nonlinear oscillator with an additional term , characterizing the isotonic oscillator, are studied. The nonlinearity affects to both the kinetic term a…
The Tremblay-Turbiner-Winternitz system on spherical and hyperbolic spaces : Superintegrability, curvature-dependent formalism and complex factorization
Manuel F. Ranada
The higher-order superintegrability of the Tremblay-Turbiner-Winternitz system (related to the harmonic oscillator) is studied on the two-dimensional spherical and hiperbolic space…
Canonoid transformations and master symmetries
José F. Cariñena, Fernando Falceto, Manuel F. Rañada
Different types of transformations of a dynamical system, that are compatible with the Hamiltonian structure, are discussed making use of a geometric formalism. Firstly, the case o…
Higher-order superintegrability of separable potentials with a new approach to the Post-Winternitz system
Manuel F. Rañada
The higher-order superintegrability of separable potentials is studied. It is proved that these potentials possess (in addition to the two quadratic integrals) a third integral of…
A new approach to the higher-order superintegrability of the Tremblay-Turbiner-Winternitz system
Manuel F. Ranada
The higher-order superintegrability of systems separable in polar coordinates is studied using an approch that was previously applied for the study of the superintegrability of a g…
The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach II
José F. Cariñena, Manuel F. Rañada, Mariano Santander
This paper is the second part of a study of the quantum free particle on spherical and hyperbolic spaces by making use of a curvature-dependent formalism. Here we study the analogu…
Curvature-dependent formalism, Schrödinger equation and energy levels for the harmonic oscillator on three-dimensional spherical and hyperbolic spaces
José F. Cariñena, Manuel F. Rañada, Mariano Santander
A nonlinear model representing the quantum harmonic oscillator on the three-dimensional spherical and hyperbolic spaces, $S_\k^3$ () and (), is studied. The curva…
A geometric approach to a generalized virial theorem
José F. Cariñena, Fernando Falceto, Manuel F. Rañada
The virial theorem, introduced by Clausius in statistical mechanics, and later applied in both classical mechanics and quantum mechanics, is studied by making use of symplectic for…
The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach
José F. Cariñena, Manuel F. Rañada, Mariano Santander
The quantum free particle on the sphere () and on the hyperbolic plane () is studied using a formalism that considers the curvature $\k$ as a parameter. T…
A geometric approach to integrability of Abel differential equations
José F. Cariñena, Javier de Lucas, Manuel F. Rañada
A geometric approach is used to study the Abel first order differential equation of the first kind. The approach is based on the recently developed theory of quasi-Lie systems whic…
A new proof of the higher-order superintegrability of a noncentral oscillator with inversely quadratic nonlinearities
Manuel F. Rañada, Miguel A. Rodríguez, Mariano Santander
The superintegrability of a rational harmonic oscillator (non-central harmonic oscillator with rational ratio of frequencies) with non-linear "centrifugal" terms is studied. In the…
Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials
José F. Cariñena, Partha Guha, Manuel F. Rañada
A geometric approach is used to study a family of higher-order nonlinear Abel equations. The inverse problem of the Lagrangian dynamics is studied in the particular case of the sec…