Dynamical systems and Poisson structures

DOI10.1063/1.3257919zbMath1304.37035arXiv0903.2909OpenAlexW2054501912MaRDI QIDQ3583689

Kostyantyn Zheltukhin, Metin Gürses, Gusein Sh. Guseinov

Publication date: 17 August 2010

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

Full work available at URL: https://arxiv.org/abs/0903.2909

zbMATH Keywords

Poisson structureslocally bi-Hamiltonian

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 (10)

Hamiltonian dynamical systems and geometry of surfaces in 3-D ⋮ Integrable Deformations of Three-Dimensional Chaotic Systems ⋮ Bifurcations of limit cycles of perturbed completely integrable systems ⋮ A normal form of completely integrable systems ⋮ Motion of an integral curve of a Hamiltonian dynamical system and the evolution equations in 3D ⋮ Generalization of the separation of variables in the Jacobi identities for finite-dimensional Poisson systems ⋮ Unnamed Item ⋮ Integrable deformations, bi-Hamiltonian structures and nonintegrability of a generalized Rikitake system ⋮ Comment on “Dynamical systems and Poisson structures” [J. Math. Phys. 50, 112703 (2009)] ⋮ Complete integrability versus symmetry

Cites Work

• The Hamiltonian structures of 3D ODE with time-independent invariants
• On the generalized Hamiltonian structure of 3D dynamical systems
• New solutions of the Jacobi equations for three-dimensional Poisson structures
• Generalized Hamiltonian Dynamics
• Hamiltonian equations in R3
• Complexified dynamical systems
• Super-integrable Calogero-type systems admit maximal number of Poisson structures
• One solution of the 3D Jacobi identities allows determining an infinity of them

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