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.

References in corpus (6)

• Simple evaluation of Casimir invariants in finite-dimensional Poisson systems
• Hamiltonian structure and Darboux theorem for families of generalized Lotka-Volterra systems
• A constant of motion in 3D implies a local generalized Hamiltonian structure
• Separation of variables in the Jacobi identities
• Local Stability and Lyapunov Functionals for n-Dimensional Quasipolynomial Conservative Systems
• Computing Casimir invariants from Pfaffian systems

Cited by in corpus (6)

• 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
• New global solutions of the Jacobi partial differential equations