Symmetries and conservation laws for the generalized n‐dimensional Ermakov system

Abstract

We revise recent results on the classification of the generalized three-dimensional Hamiltonian Ermakov system. We show that a statement published recently is incorrect, while the solution for the classification problem was incomplete. We present the correct classification for the three-dimensional system by using results which related the background space with the dynamics.Finally, we extend our results for the generalized n -dimensional Hamiltonian Ermakov system.

Modulated Kepler-Ermakov triads. Integrable Hamiltonian structure and parametrisation

“…It is remarked that there continues to be research interest in Ermakov systems and their extensions. Thus, subsequent to the extensive review of the diverse physical applications of such nonlinear systems in [25] recent developments in [37][38][39][40] may be cited.…”