One solution of the 3D Jacobi identities allows determining an infinity of them

Abstract

It is demonstrated that the knowledge of a single and arbitrary solution of the three-dimension\-al Jacobi equations allows determining infinite families of new solutions, which are generally and explicitly constructed in what follows. Examples are given.

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Cited by in corpus (12)

• Some Bi-Hamiltonian Equations in $R^3$
• Dynamical Systems and Poisson Structures
• Bi-Hamiltonian Structures of Chaotic Dynamical Systems in 3D
• 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
• On Time-dependent Hamiltonian Realizations of Planar and Nonplanar Systems
• New four-dimensional solutions of the Jacobi equations for Poisson structures
• On the quest for generalized Hamiltonian descriptions of $3D$-flows generated by curl of a vector potential
• Jacobi Structures in ${\mathbb{R}}^3$
• New global solutions of the Jacobi partial differential equations