Characterization, global analysis and integrability of a family of Poisson structures

Abstract

An n-dimensional solution family of the Jacobi equations is characterized and investigated, including the global determination of its main features: the Casimir invariants, the construction of the Darboux canonical form and the proof of integrability for the related Poisson systems. Examples are given and include novel Poisson formulations.

arXiv admin note: text overlap with arXiv:1910.05141

References in corpus (11)

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• Hamiltonian structure and Darboux theorem for families of generalized Lotka-Volterra systems
• New solutions of the Jacobi equations for three-dimensional Poisson structures
• A constant of motion in 3D implies a local generalized Hamiltonian structure
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• Characterization and global analysis of a family of Poisson structures
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Cited by in corpus (6)

• Generalization of solutions of the Jacobi PDEs associated to time reparametrizations of Poisson systems
• Generalized results on the role of new-time transformations in finite-dimensional Poisson systems
• Poisson systems as the natural framework for additional first integrals via Darboux invariant hypersurfaces
• Generalization of the separation of variables in the Jacobi identities for finite-dimensional Poisson systems
• New global solutions of the Jacobi partial differential equations
• Congruence method for global Darboux reduction of finite-dimensional Poisson systems