American Institute of Mathematical Sciences

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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

A.V. Borisov 1, , A.A. Kilin 1, and  I.S. Mamaev 1,

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.
Keywords: Vortex dynamics, point vortices., reduction, Poincar¶e map.
Mathematics Subject Classification: 37N10, 76B4.
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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