This article is cited in 4 scientific papers (total in 4 papers)
Reduction and chaotic behavior of point vortices on a plane and a sphere
A. V. Borisovab, A. A. Kilinab, I. S. Mamaevab
a Udmurt State University
b Institute of Computer Science
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.
reduction, point vortex, equations of motion, Poincaré map.
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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”, Nelin. Dinam., 1:2 (2005), 233–246
Citation in format AMSBIB
\by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev
\paper Reduction and chaotic behavior of point vortices on a plane and a sphere
\jour Nelin. Dinam.
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Vetchanin E.V., Kazakov A.O., “Bifurcations and Chaos in the Dynamics of Two Point Vortices in An Acoustic Wave”, Int. J. Bifurcation Chaos, 26:4 (2016), 1650063
Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “Three Vortices in Spaces of Constant Curvature: Reduction, Poisson Geometry, and Stability”, Regul. Chaotic Dyn., 23:5 (2018), 613–636
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