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

A. V. Borisov·A. A. Kilin·I. S. Mamaev
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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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A. V. Borisov, A. A. Kilin, I. S. Mamaev. 2005-07-26. Reduction and chaotic behavior of point vortices on a plane and a sphere. https://arxiv.org/abs/nlin/0507057

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