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- W2054501912 abstract "We first consider the Hamiltonian formulation of $n=3$ systems in general and show that all dynamical systems in ${mathbb R}^3$ are bi-Hamiltonian. An algorithm is introduced to obtain Poisson structures of a given dynamical system. We find the Poisson structures of a dynamical system recently given by Bender et al. Secondly, we show that all dynamical systems in ${mathbb R}^n$ are $(n-1)$-Hamiltonian. We give also an algorithm, similar to the case in ${mathbb R}^3$, to construct a rank two Poisson structure of dynamical systems in ${mathbb R}^n$. We give a classification of the dynamical systems with respect to the invariant functions of the vector field $vec{X}$ and show that all autonomous dynamical systems in ${mathbb R}^n$ are super-integrable." @default.
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- W2054501912 date "2009-11-01" @default.
- W2054501912 modified "2023-10-16" @default.
- W2054501912 title "Dynamical systems and Poisson structures" @default.
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- W2054501912 doi "https://doi.org/10.1063/1.3257919" @default.
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