Some ring-shaped potentials as a generalized 4-D isotropic oscillator. Periodic orbits

Eva Tresaco (1) , Sebastián Ferrer (2)

1 Dpto. de Matemática Aplicada
2 Dpto. de Matemática Aplicada

A generalized integrable biparametric family of 4-D isotropic oscillators is proposed. It allows to treat in a unified way, Pöschl-Teller, Hartmann and other ring-shaped systems. This approach, based in the use of two canonical extensions, helps to simplify the studies of classical aspects of those systems. As an illustration, an analysis of the periodic solutions of those system is presented.

Mots clés: 4-D isotropic oscillators; Generalized Hartmann potential; Ring-shaped systems; Pöschl-Teller potential; Superintegrability

Eva Tresaco, Sebastián Ferrer. Some ring-shaped potentials as a generalized 4-D isotropic oscillator. Periodic orbits. Celestial Mechanics and Dynamical Astronomy, 2010, 107 (3), pp.337-352. ⟨10.1007/s10569-010-9258-6⟩. ⟨hal-00552501⟩