|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Peer-reviewed Journal Articles, etc >
Chaotic motion of the N-vortex problem on a sphere: II. Saddle centers in three-degree-of-freedom Hamiltonians
| Title: | Chaotic motion of the N-vortex problem on a sphere: II. Saddle centers in three-degree-of-freedom Hamiltonians |
| Authors: | Sakajo, Takashi Browse this author →KAKEN DB | | Yagasaki, Kazuyuki Browse this author |
| Keywords: | Point vortex | | Flows on sphere | | Chaos | | Saddle centers |
| Issue Date: | 15-Aug-2008 |
| Publisher: | Elsevier B.V. |
| Journal Title: | Physica D Nonlinear Phenomena |
| Volume: | 237 |
| Issue: | 14-17 |
| Start Page: | 2078 |
| End Page: | 2083 |
| Publisher DOI: | 10.1016/j.physd.2008.02.001 |
| Abstract: | This paper deals with complicated behavior in the N=8n vortex problem on a sphere, which is reduced to three-degree-of-freedom Hamiltonian systems. In the reduced Hamiltonians, the polygonal ring configuration of the point vortices becomes a saddle-center equilibrium which has two hyperbolic and four center directions in some parameter regions. Near the saddle center, there exists a normally hyperbolic, locally invariant manifold including a Cantor set of whiskered tori. For N=8 we numerically compute the stable and unstable manifolds of the locally invariant manifold with the assistance of the center manifold technique, and show that they intersect transversely and complicated dynamics may occur. Direct numerical simulations are also given to demonstrate our numerical analysis. |
| Relation: | http://www.sciencedirect.com/science/journal/01672789 |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/34774 |
| 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)
|
Submitter: 坂上 貴之
|
