A constant of motion in 3D implies a local generalized Hamiltonian structure

Abstract

We demonstrate that a Poisson structure can always be associated to a general nonautonomous 3D vector field of ODEs by means of a diffeomorphism that preserves both the orientation and the volume of phase-space. The only prerequisite is the existence of one constant of motion.

References in corpus (1)

• Nonpolynomial vector fields under the Lotka-Volterra normal form

Cited by in corpus (13)

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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
• Characterization, global analysis and integrability of a family of Poisson structures
• New four-dimensional solutions of the Jacobi equations for Poisson structures
• Quasipolynomial generalization of Lotka-Volterra mappings
• New global solutions of the Jacobi partial differential equations
• Bi-Hamiltonian Structure in Serret-Frenet Frame
• Bi-Hamiltonian Structure of Gradient Systems in Three Dimensions and Geometry of Potential Surfaces