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Invariant dynamical systems embedded in the N-vortex problem on a sphere with pole vortices
Title: | Invariant dynamical systems embedded in the N-vortex problem on a sphere with pole vortices |
Authors: | Sakajo, Takashi Browse this author →KAKEN DB |
Keywords: | Vortex points | Flow on a sphere | Reduction method | Invariant dynamical systems |
Issue Date: | May-2006 |
Publisher: | Elsevier |
Journal Title: | Physica D: Nonlinear Phenomena |
Volume: | 217 |
Issue: | 2 |
Start Page: | 142 |
End Page: | 152 |
Publisher DOI: | 10.1016/j.physd.2006.04.002 |
Abstract: | We are concerned with the system of N vortex points on a sphere with two fixed vortex points at the poles. This article gives a reduction method of the system to invariant dynamical systems when all the vortex points have the same strength. It is carried out by considering the invariant property of the system with respect to the shift and pole reversal transformations, for which the polygonal ring configuration of the N vortex points at the line of latitude, called "N-ring", remains unchanged. We prove that there exists a 2p-dimensional invariant dynamical system reduced by the p-shift transformation for arbitrary factor p of N. The p-shift invariant system is equivalent to the p-vortex points system generated by the averaged Hamiltonian with the modified pole vortices. It is also shown that the system can be reduced by the pole reversal transformation when the pole vortices are identical. Since the reduced dynamical systems are defined in the linear space spanned by the eigenvectors given in the linear stability analysis for the N-ring, we obtain the inclusion relation among the invariant reduced dynamical systems. This allows us to decompose the system of a large number of vortex points into a collection of invariant reduced subsystems. |
Description: | PACS: 47.32.Cc 47.20.Ky,05.45.-a |
Relation: | http://www.sciencedirect.com/science/journal/01672789 |
Type: | article (author version) |
URI: | http://hdl.handle.net/2115/8557 |
Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 坂上 貴之
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