Generalized Hamiltonian structures for Ermakov systems

Abstract

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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Cited by in corpus (5)

• Characterization and global analysis of a family of Poisson structures
• Ermakov-Lewis Invariants and Reid Systems
• New solution family of the Jacobi equations: Characterization, invariants, and global Darboux analysis
• Weak measurements of trajectories in quantum systems: classical, Bohmian and sum over paths
• New four-dimensional solutions of the Jacobi equations for Poisson structures