Modulated Kepler-Ermakov triads. Integrable Hamiltonian structure and parametrisation

Abstract

A hybrid Kepler-Ermakov system modulated by means of a classical nonlinear superposition principle is reduced via a class of involutory transformations to its unmodulated counterpart. In the case of certain underlying Hamiltonian-type and dual associated structure, parametric representations are applied which allow systematic integration on application of admitted invariants.