New solutions of the Jacobi equations for three-dimensional Poisson structures

DOI10.1063/1.1402174zbMath1047.70040arXiv1910.03314OpenAlexW3104005308MaRDI QIDQ2774704

Benito Hernández-Bermejo

Publication date: 26 February 2002

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.03314

zbMATH Keywords

symplectic structureCasimir invariantsDarboux canonical form

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45)

Related Items (21)

$3D$-flows generated by the curl of a vector potential & Maurer-Cartan equations ⋮ Nekhoroshev and KAM stabilities in generalized Hamiltonian systems ⋮ Bi-Hamiltonian Structures of 3D Chaotic Dynamical Systems ⋮ Direct Poisson neural networks: learning non-symplectic mechanical systems ⋮ New global solutions of the Jacobi partial differential equations ⋮ KAM in generalized Hamiltonian systems with multi-scales ⋮ Generalization of the separation of variables in the Jacobi identities for finite-dimensional Poisson systems ⋮ Perturbed Euler top and bifurcation of limit cycles on invariant Casimir surfaces ⋮ Generalization of solutions of the Jacobi PDEs associated to time reparametrizations of Poisson systems ⋮ Realization of tangent perturbations in discrete and continuous time conservative systems ⋮ On time-dependent Hamiltonian realizations of planar and nonplanar systems ⋮ Dynamical systems and Poisson structures ⋮ Characterization, global analysis and integrability of a family of Poisson structures ⋮ Global existence of bi-Hamiltonian structures on orientable three-dimensional manifolds ⋮ Characterization and global analysis of a family of Poisson structures ⋮ ON PLANAR AND NON-PLANAR ISOCHRONOUS SYSTEMS AND POISSON STRUCTURES ⋮ Bi-Hamiltonian structure in Frenet-Serret frame ⋮ Generalized results on the role of new-time transformations in finite-dimensional Poisson systems ⋮ On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D ⋮ Jacobi structures in R3 ⋮ New four-dimensional solutions of the Jacobi equations for Poisson structures

Cites Work

• Hamiltonian chaos in nonlinear optical polarization dynamics
• The Hamiltonian structure of the Maxwell-Vlasov equations
• Separation of variables in the Jacobi identities
• Hamiltonian structure and first integrals for the Lotka-Volterra systems
• Lie-Poisson description of Hamiltonian ray optics
• On quadratic Poisson structures
• Multiple Lie-Poisson structures, reductions, and geometric phases for the Maxwell-Bloch travelling wave equations
• Stability of relative equilibria. II: Application to nonlinear elasticity
• Classification and Casimir invariants of Lie-Poisson brackets
• On the generalized Hamiltonian structure of 3D dynamical systems
• Bi-Hamiltonian structure of the Kermack-McKendrick model for epidemics
• Hamiltonian perturbation theory in noncanonical coordinates
• Hamiltonian formulation of reduced magnetohydrodynamics
• Stability and bifurcation of a rotating planar liquid drop
• On the construction of Hamiltonians
• Quadratic Poisson structures
• The Hamiltonization problem from a global viewpoint
• On the Hamiltonian structure of 2D ODE possessing an invariant
• A simple model of the integrable Hamiltonian equation
• The construction of a Poisson structure out of a symmetry and a conservation law of a dynamical system
• On the Dynamics of Lotka--Volterra Equations Having an Invariant Hyperplane
• Poisson structure of dynamical systems with three degrees of freedom
• Bi-Hamiltonian systems and Lotka - Volterra equations: a three-dimensional classification
• Hamiltonian structure and Darboux theorem for families of generalized Lotka–Volterra systems
• Hamiltonian structures for the n-dimensional Lotka–Volterra equations
• Generalized Hamiltonian structures for systems in three dimensions with a rescalable constant of motion
• Quantum algebras in classical mechanics

This page was built for publication: New solutions of the Jacobi equations for three-dimensional Poisson structures