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On the generalized Hamiltonian structure of 3D dynamical systems. (English) Zbl 1020.35533

Summary: The Poisson structures for 3D systems possessing one constant of motion can always be constructed from the solution of a linear PDE. When two constants of the motion are available the problem reduces to a quadrature and the structure functions include an arbitrary function of them.

MSC:

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
35Q99 Partial differential equations of mathematical physics and other areas of application
70H05 Hamilton’s equations
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