### A new proof of the higher-order superintegrability of a noncentral oscillator with inversely quadratic nonlinearitiesA new proof of the higher-order superintegrability of a noncentral oscillator with inversely quadratic nonlinearities

Access Restriction
Open

 Author Rañada, Manuel F. ♦ Rodríguez, Miguel A. ♦ Santander, Mariano Source arXiv.org Content type Text File Format PDF Date of Submission 2010-02-20 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Mathematics ♦ Physics Subject Keyword Mathematical Physics ♦ 37J35 ♦ 70H06 ♦ math ♦ physics:math-ph Abstract 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 first part, the system is directly studied in the Euclidean plane; the existence of higher-order superintegrability (integrals of motion of higher order than 2 in the momenta) is proved by introducing a deformation in the quadratic complex equation of the linear system. The constants of motion of the nonlinear system are explicitly obtained. In the second part, the inverse problem is analyzed in the general case of $n$ degrees of freedom; starting with a general Hamiltonian $H$, and introducing appropriate conditions for obtaining superintegrability, the particular "centrifugal" nonlinearities are obtained. Description Reference: J. Math. Phys., no. 4, 042901 (2010) Educational Use Research Learning Resource Type Article Page Count 16