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Chaotic Motion of the N-Vortex Problem on a Sphere: I. Saddle-Centers in Two-Degree-of-Freedom Hamiltonians.
- Source :
-
Journal of Nonlinear Science . Oct2008, Vol. 18 Issue 5, p485-525. 41p. 5 Diagrams, 2 Charts, 13 Graphs. - Publication Year :
- 2008
-
Abstract
- We study the motion of N point vortices with Nāā 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=5 n or 6 n with nāā, 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SPHERES
*VORTEX motion
*DEGREES of freedom
*CHAOS theory
*MATHEMATICAL models
Subjects
Details
- Language :
- English
- ISSN :
- 09388974
- Volume :
- 18
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Journal of Nonlinear Science
- Publication Type :
- Academic Journal
- Accession number :
- 34873726
- Full Text :
- https://doi.org/10.1007/s00332-008-9019-9