On the generalized Hamiltonian structure of 3D dynamical systems

DOI10.1016/0375-9601(95)00113-HzbMath1020.35533arXivmath-ph/0211035WikidataQ62038664 ScholiaQ62038664MaRDI QIDQ1965492

F. Haas, João Goedert

Publication date: 8 February 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0211035

Mathematics Subject Classification ID

Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (18)

Comments on Hamiltonian structures for the n-dimensional Lotka–Volterra equations [J. Math. Phys. 36, 3520–3534 (1995)] ⋮ Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers ⋮ Hamiltonian dynamical systems and geometry of surfaces in 3-D ⋮ A constant of motion in 3D implies a local generalized Hamiltonian structure. ⋮ Generalization of solutions of the Jacobi PDEs associated to time reparametrizations of Poisson systems ⋮ A Hamilton-Poisson model of the Chen-Lee system ⋮ Hamilton-Poisson realizations for the Lü system ⋮ Dynamical systems and Poisson structures ⋮ Global existence of bi-Hamiltonian structures on orientable three-dimensional manifolds ⋮ New solutions of the Jacobi equations for three-dimensional Poisson structures ⋮ Characterization and global analysis of a family of Poisson structures ⋮ One solution of the 3D Jacobi identities allows determining an infinity of them ⋮ Bi-Hamiltonian structure and homoclinic orbits of the Maxwell--Bloch equations with RWA ⋮ Simple evaluation of Casimir invariants in finite-dimensional Poisson systems ⋮ Separation of variables in the Jacobi identities ⋮ Bi-Hamiltonian structure in Frenet-Serret frame ⋮ Comment on “Dynamical systems and Poisson structures” [J. Math. Phys. 50, 112703 (2009)] ⋮ Jacobi structures in R3

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• On the construction of Hamiltonians
• The Hamiltonization problem from a global viewpoint
• Integrals of motion for three-dimensional non-Hamiltonian dynamical systems
• Families of invariants of the motion for the Lotka–Volterra equations: The linear polynomials family
• Poisson structure of dynamical systems with three degrees of freedom
• Deterministic Nonperiodic Flow
• Generalized Hamiltonian structures for systems in three dimensions with a rescalable constant of motion
• Quantum algebras in classical mechanics

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