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High-dimensional heteroclinic and homoclinic connections in odd point-vortex ring on a sphere
| Title: | High-dimensional heteroclinic and homoclinic connections in odd point-vortex ring on a sphere |
| Authors: | Sakajo, Takashi1 Browse this author →KAKEN DB |
| Authors(alt): | 坂上, 貴之1 |
| Keywords: | Vortex points | | Flow on a sphere | | Heteroclinic manifold | | Projection method |
| Issue Date: | Jan-2006 |
| Publisher: | Institute of Physics |
| Journal Title: | Nonlinearity |
| Volume: | 19 |
| Issue: | 1 |
| Start Page: | 75 |
| End Page: | 93 |
| Publisher DOI: | 10.1088/0951-7715/19/1/005 |
| Abstract: | We consider the motion of the N-vortex points that are equally spaced along a line of latitude on sphere with fixed pole vortices, called "N-ring". We are especially interested in the case when the number of the vortex points is odd. Since the eigenvalues that determine the stability of the odd N- ring are double, each of the unstable and stable manifolds corresponding to them is two-dimensional. Hence, it is generally difficult to describe the global structure of the manifolds. In this article, based on the linear stability analysis, we propose a projection method to observe the structure of the iso-surface of the Hamiltonian, in which the orbit of the vortex points evolves. Applying the projection method to the motion of the 3-ring and 5-ring, we characterize the complex evolution of the unstable odd N-ring from the topological structure of the iso-surface of the Hamiltonian. |
| Description URI: | http://www.iop.org/ |
| Rights: | Copyright © 2006 IOP Publishing Ltd. |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/5417 |
| 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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