Separation of variables in the Jacobi identities

Abstract

A new family of $n$-dimensional solutions of the Jacobi identities is characterized. Such a family is very general, thus unifying in a common framework many different well-known Poisson systems seemingly unrelated. This unification is not only conceptual, but also allows the development of general global methods of analysis.

References in corpus (4)

• Multiple Hamiltonian Structures for Toda-type systems
• Simple evaluation of Casimir invariants in finite-dimensional Poisson systems
• Hamiltonian structure and Darboux theorem for families of generalized Lotka-Volterra systems
• Computing Casimir invariants from Pfaffian systems

Cited by in corpus (13)

• New solutions of the Jacobi equations for three-dimensional Poisson structures
• One solution of the 3D Jacobi identities allows determining an infinity of them
• 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
• An integrable family of Poisson systems: Characterization and global analysis
• New four-dimensional solutions of the Jacobi equations for Poisson structures
• New global solutions of the Jacobi partial differential equations
• Generalization of the separation of variables in the Jacobi identities for finite-dimensional Poisson systems
• Bi-Hamiltonian Structure in Serret-Frenet Frame
• Congruence method for global Darboux reduction of finite-dimensional Poisson systems
• Bi-Hamiltonian Structure of Gradient Systems in Three Dimensions and Geometry of Potential Surfaces