On the generalized Hamiltonian structure of 3D dynamical systems

Abstract

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.

Cited by in corpus (17)

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• Separation of variables in the Jacobi identities
• One solution of the 3D Jacobi identities allows determining an infinity of them
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• Characterization and global analysis of a family of Poisson structures
• Generalization of solutions of the Jacobi PDEs associated to time reparametrizations of Poisson systems
• New solution family of the Jacobi equations: Characterization, invariants, and global Darboux analysis
• New four-dimensional solutions of the Jacobi equations for Poisson structures
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• Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds
• Bi-Hamiltonian Structure in Serret-Frenet Frame
• Poisson Structures for Aristotelian Model of Three Body Motion
• Bi-Hamiltonian Structure of Gradient Systems in Three Dimensions and Geometry of Potential Surfaces