Abstract
We have proved that any 3-dimensional dynamical system of ordinary differential equations (in short, 3D ODE) with time-independent invariants can be rewritten as Hamiltonian systems with respect to generalized Poisson brackets and the Hamiltonians are these invariants. As an example, we discuss the Kermack-Mckendrick model for epidemics in detail. The results we obtained are generalization of those obtained by Y. Nutku.
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First Received Nov. 22, 1993
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Zhong-heng, G., Yu-ming, C. The Hamiltonian structures of 3D ODE with time-independent invariants. Appl Math Mech 16, 301–306 (1995). https://doi.org/10.1007/BF02456942
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DOI: https://doi.org/10.1007/BF02456942