Chaotic Motion of the N-Vortex Problem on a Sphere: I.Saddle-Centers in Two-Degree-of-Freedom Hamiltonians
抄録
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.
収録刊行物
-
- Journal of Nonlinear Science
-
Journal of Nonlinear Science 18 485-525, 2008-03-04
Springer New York
- Tweet
詳細情報
-
- CRID
- 1050845763927590016
-
- NII論文ID
- 120000947329
-
- ISSN
- 14321467
- 09388974
-
- HANDLE
- 2115/34776
-
- 本文言語コード
- en
-
- 資料種別
- journal article
-
- データソース種別
-
- IRDB
- CiNii Articles
- KAKEN