Existence of KAM tori in the phase-space of lattice vortex systems

DOI10.1007/BF00945109zbMath0850.70183MaRDI QIDQ1813932

Chjan C. Lim

Publication date: 25 June 1992

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Mathematics Subject Classification ID

Hamilton's equations (70H05) Dynamical systems and ergodic theory (37-XX)

Related Items

Graph theory and a special class of symplectic transformations: The generalized Jacobi variables ⋮ Global Phase Diagrams of Three Point Vortices ⋮ Explicit nondegeneracy conditions of KAM tori for the planar N-point vortex systems ⋮ Studies of perturbed three vortex dynamics ⋮ Relative equilibria of point vortices on the sphere ⋮ General Jacobi coordinates and Herman resonance for some nonheliocentric celestial \(N\)-body problems ⋮ The \(n\)-vortex problem on a Riemann sphere ⋮ Chaotic motion of the \(N\)-vortex problem on a sphere. I. Saddle-centers in two-degree-of-freedom Hamiltonians ⋮ Generalized point vortex dynamics on \(\mathbb{CP}^2\) ⋮ Binary trees, symplectic matrices and the Jacobi coordinates of celestial mechanics ⋮ KAM theory analysis of the dynamics of three coaxial vortex rings ⋮ Transition from Quasiperiodicity to Chaos for Three Coaxial Vortex Rings

Cites Work

• Desingularizations of systems of point vortices
• Quasi-periodic dynamics of desingularized vortex models
• Stable and Random Motions in Dynamical Systems
• A study of singularity formation in a vortex sheet by the point-vortex approximation
• A moment model for vortex interactions of the two-dimensional Euler equations. Part 1. Computational validation of a Hamiltonian elliptical representation
• Convergence of the Vortex Method for Vortex Sheets
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
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