Note on invariants for uncoupled Ermakov systems

Authors: Thylwe, K.-E.
Document Type: Article
Pubstate: Published
Journal: J. Phys. A: Math. Gen
Volume: 35   4359-4362
Year: 2002


Several invariants for an Ermakov system consisting of a parametric oscillator and a Milne oscillator in one dimension are derived. This system appears in amplitude-phase analysis of parametric oscillator solutions. First- and second-order invariants for such a system are derived using the Wronskian relations of a fundamental pair of parametric oscillator solutions. In this way Wronskian invariants of the parametric oscillator system alone imply Ermakov-Lewis type invariants for the combined Ermakov system, as well as invariants for the Milne system alone.