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

Borisov, A. V.; Kilin, A. A.; Mamaev, I. S.

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

Authors

Borisov, A. V.

Kilin, A. A.

Mamaev, I. S.

Description

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.
10 pages, 3 figures