Singular manifolds and quasi-periodic solutions of Hamiltonians for vortex lattices

DOI10.1016/0167-2789(88)90025-5zbMath0659.70015OpenAlexW2009121073MaRDI QIDQ1112635

Chjan C. Lim

Publication date: 1988

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://hdl.handle.net/2027.42/27359

zbMATH Keywords

Hamiltonian systemscanonical transformationssingular manifoldsvortex latticesexistence of quasi-periodic solutionssingular weakly coupled oscillators

Mathematics Subject Classification ID

Hamilton's equations (70H05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (4)

A combinatorial perturbation method and Arnold's whiskered tori in vortex dynamics ⋮ On singular Hamiltonians: the existence of quasi-periodic solutions and nonlinear stability ⋮ Chaotic motion of the \(N\)-vortex problem on a sphere. I. Saddle-centers in two-degree-of-freedom Hamiltonians ⋮ Quasi-periodic dynamics of desingularized vortex models

Cites Work

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• How a swing behaves
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• On averaging, reduction, and symmetry in Hamiltonian systems
• On resonant non linearly coupled oscillators with two equal frequencies
• On resonant classical Hamiltonians with two equal frequencies
• Stable and Random Motions in Dynamical Systems
• Nonlinear vortex trail dynamics
• Motion of three vortices
• Bounded and unbounded solutions of the von Kármán vortex trail
• On The Motion of Three Vortices
• Periodic solutions of the N-body problem

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