A normal form of completely integrable systems

DOI10.1016/j.geomphys.2011.12.003zbMath1238.37016arXiv1106.5044OpenAlexW2140756914MaRDI QIDQ413693

Răzvan M. Tudoran

Publication date: 7 May 2012

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.5044

zbMATH Keywords

integrable systemsHamiltonian dynamicslinear normal forms

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06)

Related Items (12)

Stability and energy-Casimir mapping for integrable deformations of the Kermack-McKendrick system ⋮ Integrable Deformations of Three-Dimensional Chaotic Systems ⋮ A stability criterion for non-degenerate equilibrium states of completely integrable systems ⋮ Asymptotic stabilization with phase of periodic orbits of three-dimensional Hamiltonian systems ⋮ Integrability of a class of \(N\)-dimensional Lotka-Volterra and Kolmogorov systems ⋮ Bifurcations of limit cycles of perturbed completely integrable systems ⋮ The free rigid body dynamics: Generalized versus classic ⋮ A method to generate first integrals from infinitesimal symmetries ⋮ Complete integrability of vector fields in \(\mathbb{R}^N\) ⋮ Explicit Hamiltonian realizations of non-degenerate three-dimensional real linear differential systems ⋮ Affine distributions on Riemannian manifolds with applications to dissipative dynamics ⋮ Complete integrability versus symmetry

Cites Work

• On foundation of the generalized Nambu mechanics
• On the planar integrable differential systems
• Dynamical systems and Poisson structures
• Generalized Hamiltonian Dynamics
• Hamiltonian equations in R3
• Lotka–Volterra systems integrable in quadratures
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