Abstract
In this paper, we express the differential equations of a noncentral dynamical system in Ermakov formalism to obtain the Ermakov invariant. In term of Hamiltonian theories and using the Ermakov invariant as the Hamiltonian, the Poisson structure of a noncentral dynamical system in four-dimensional phase space are constructed. The result indicates that the Poisson structure is degenerate and the noncentral dynamical system possesses four invariants: the Hamiltonian, the Ermakov invariant and two Casimir functions.
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