|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
Chaotic motion of the N-vortex problem on a sphere I: Saddle-centers in two-degree-of-freedom
| Title: | Chaotic motion of the N-vortex problem on a sphere I: Saddle-centers in two-degree-of-freedom |
| Authors: | SAKAJO, Takashi Browse this author | | YAGASAKI, Kazuyuki Browse this author |
| Keywords: | Hamiltonian system | | point vortex | | flow on sphere | | chaos | | Melnikov method |
| Issue Date: | 6-Jun-2007 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 858 |
| Start Page: | 1 |
| End Page: | 34 |
| Abstract: | We study the motion of N point vortices with N∈ℕ on a sphere in the presence of fixed pole vortices, which are governed by a Hamiltonian dynamical system with N degrees of freedom. Special attention is paid to the evolution of their polygonal ring configuration called the N-ring, in which they are equally spaced along a line of latitude of the sphere. When the number of the point vortices is N=5n or 6n with n∈ℕ, the system is reduced to a two-degree-of-freedom Hamiltonian with some saddle-center equilibria, one of which corresponds to the unstable N-ring. Using a Melnikov-type method applicable to two-degree-of-freedom Hamiltonian systems with saddle-center equilibria and a numerical method to compute stable and unstable manifolds, we show numerically that there exist transverse homoclinic orbits to unstable periodic orbits in the neighborhood of the saddle-centers and hence chaotic motions occur. Especially, the evolution of the unstable N-ring is shown to be chaotic. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69667 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
|
Submitter: 数学紀要登録作業用
|
