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New periodic solutions for three or four identical vortices on a plane and a sphere

Pages: 110 - 120, Issue Special, August 2005

 Abstract        Full Text (205.8K)              

A.V. Borisov - Institute of Computer Science, Udmurt State University, 426034 Izhevsk, Russian Federation (email)
I.S. Mamaev - Institute of Computer Science, Udmurt State University, 426034 Izhevsk, Russian Federation (email)
A.A. Kilin - Institute of Computer Science, Udmurt State University, 426034 Izhevsk, Russian Federation (email)

Abstract: In this paper we describe new classes of periodic solutions for point vortices on a plane and a sphere. They correspond to similar solutions (so-called choreographies) in celestial mechanics.

Keywords:  periodic solutions, choreographies, vortex dynamics, reduction.
Mathematics Subject Classification:  37N10, 76B47.

Received: September 2004;      Revised: April 2005;      Published: September 2005.