Computing Casimir invariants from Pfaffian systems

Abstract

We describe a method for computing Casimir invariants that is applicable to both finite and infinite-dimensional Poisson brackets. We apply the method to various finite and infinite-dimensional examples, including a Poisson bracket embodying both finite and infinite-dimensional structure.

References in corpus (2)

• Simple evaluation of Casimir invariants in finite-dimensional Poisson systems
• Hamiltonian structure and Darboux theorem for families of generalized Lotka-Volterra systems

Cited by in corpus (7)

• New solutions of the Jacobi equations for three-dimensional Poisson structures
• Separation of variables in the Jacobi identities
• One solution of the 3D Jacobi identities allows determining an infinity of them
• New solution family of the Jacobi equations: Characterization, invariants, and global Darboux analysis
• New four-dimensional solutions of the Jacobi equations for Poisson structures
• New global solutions of the Jacobi partial differential equations
• Casimir operators induced by Maurer-Cartan equations