Singular manifolds and quasi-periodic solutions of Hamiltonians for vortex lattices
type: Item
instance of: scholarly article
title: Singular manifolds and quasi-periodic solutions of Hamiltonians for vortex lattices
zbMATH Open document ID: 0659.70015
DOI: 10.1016/0167-2789(88)90025-5
author: Chjan C. Lim
published in: Physica D
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://hdl.handle.net/2027.42/27359
review text: A general method for establishing the existence of quasi-periodic solutions of Hamiltonian systems for vortex lattices is illustrated in a simple example involving two degrees of freedom. The geometry of intersecting singular manifolds of the Hamiltonians introduces suitable canonical transformations which put the Hamiltonian into the form of singular weakly coupled oscillators. As by-products of this procedure, additional integrals of motion are found for the leading term in the transformed Hamiltonian. These extra integrals are approximate invariants for the full Hamiltonians.
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 70H15
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 4078880
zbMATH Keywords: existence of quasi-periodic solutions
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: vortex lattices
zbMATH Keywords: singular manifolds
zbMATH Keywords: canonical transformations
zbMATH Keywords: singular weakly coupled oscillators
MaRDI profile type: Publication
OpenAlex ID: W2009121073
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description: scientific article; zbMATH DE number 4078880