Reduction and chaotic behavior of point vortices on a plane and a sphere

2005/07/26 by A. V. Borisov, Borisov, A. V., A. A. Kilin +3
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0507057

10 pages, 3 figures

arxiv created 2005/07/26 · arxiv updated 2009/12/01

Abstract

We offer a new method of reduction for a system of point vortices on a plane and a sphere. This method is similar to the classical node elimination procedure. However, as applied to the vortex dynamics, it requires substantial modification. Reduction of four vortices on a sphere is given in more detail. We also use the Poincare surface-of-section technique to perform the reduction a four-vortex system on a sphere.

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