Chaotic motion of the \(N\)-vortex problem on a sphere. I. Saddle-centers in two-degree-of-freedom Hamiltonians
type: Item
instance of: scholarly article
title: Chaotic motion of the \(N\)-vortex problem on a sphere. I. Saddle-centers in two-degree-of-freedom Hamiltonians
zbMATH Open document ID: 1168.37026
author: Takashi Sakajo
author: Kazuyuki Yagasaki
published in: Journal of Nonlinear Science
publication date: 2009-05-08T00:00:00Z
review text: The motion of \(N (N\in N)\) point vortices on a sphere in the presence of fixed pole vortices is shown in this work. Special attention is paid to the evolution of their configuration, in which they are equally spaced along a line of latitude of the sphere. When \(N = 5n\) and \(6n\) with \(n\in N\), the system is reduced to a two degree of freedom Hamiltonian with saddle-center equilibria, one of which corresponds to the unstable \(N -ring\). To compute stable and unstable manifolds , it is shown numerically that there exist transverse homoclinic orbits to unstable periodic orbits in the neighborhood of the saddle-centers and hence chaotic motions occur. The basic results are presented in: 2 tables, 18 figures, 2 appendixes, 5 propositions, 2 lemmas and 2 theorems.
reviewed by: Gasanbek T. Arazov
Mathematics Subject Classification ID: 37N10
zbMATH DE Number: 5552199
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: Point vortex
zbMATH Keywords: Flow on sphere
zbMATH Keywords: Chaos
describes a project that uses: Dynamics
describes a project that uses: HomCont
describes a project that uses: AUTO
MaRDI profile type: Publication
full work available at URL: s00332-008-9019-9
OpenAlex ID: W2052869340
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DOI: 10.1007/S00332-008-9019-9
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description: scientific article; zbMATH DE number 5552199