Geodesic
Reduction and chaotic behavior of point vortices on a plane and a sphere
Russian journal of nonlinear dynamics, Tome 1 (2005) no. 2, pp. 233-246.

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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 Poincaré surface-of-section technique to perform the reduction a four-vortex system on a sphere.
Keywords: reduction, Poincaré map.
Mots-clés : point vortex, equations of motion 
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A. V. Borisov; A. A. Kilin; I. S. Mamaev. Reduction and chaotic behavior of point vortices on a plane and a sphere. Russian journal of nonlinear dynamics, Tome 1 (2005) no. 2, pp. 233-246. http://geodesic.mathdoc.fr/item/ND_2005_1_2_a5/