Jacobi Structures in ${\mathbb{R}}^3$

Abstract

The most general Jacobi brackets in ${\mathbb{R}}^3$ are constructed after solving the equations imposed by the Jacobi identity. Two classes of Jacobi brackets were identified, according to the rank of the Jacobi structures. The associated Hamiltonian vector fields are also constructed.

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Cited by in corpus (3)

• Jacobi structures on real two- and three-dimensional Lie groups and their Jacobi-Lie systems
• Classical r-matrices of real low-dimensional Jacobi-Lie bialgebras and their Jacobi-Lie groups
• Integrable bi-Hamiltonian systems by Jacobi structure on real three-dimensional Lie groups