Generalized Hamiltonian structures for Ermakov systems

Details Generalized Hamiltonian structures for Ermakov systems Generalized Hamiltonian structures for Ermakov systems

2002-11-17

arxiv.org/abs/math-ph/0211033v1

J. Phys. A: Math. Gen. v. 35 (2002) 2925-2935

Physics

Mathematical Physics

Scientific paper

10.1088/0305-4470/35/12/314

We construct Poisson structures for Ermakov systems, using the Ermakov invariant as the Hamiltonian. Two classes of Poisson structures are obtained, one of them degenerate, in which case we derive the Casimir functions. In some situations, the existence of Casimir functions can give rise to superintegrable Ermakov systems. Finally, we characterize the cases where linearization of the equations of motion is possible.

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