# American Institute of Mathematical Sciences

2005, 2005(Special): 100-109. doi: 10.3934/proc.2005.2005.100

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

 1 Institute of Computer Science, Udmurt State University, 426034 Izhevsk, Russian Federation, Russian Federation, Russian Federation

Received  September 2004 Revised  April 2005 Published  September 2005

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.
Citation: A.V. Borisov, A.A. Kilin, I.S. Mamaev. Reduction and chaotic behavior of point vortices on a plane and a sphere. Conference Publications, 2005, 2005 (Special) : 100-109. doi: 10.3934/proc.2005.2005.100
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