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Nelin. Dinam., 2005, Volume 1, Number 2, Pages 233–246 (Mi nd201)  

This article is cited in 3 scientific papers (total in 3 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

Abstract: 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: reduction, point vortex, equations of motion, Poincaré map.

Full text: PDF file (473 kB)

Document Type: Article
UDC: 532.5.013

Citation: 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
\Bibitem{BorKilMam05}
\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.
\yr 2005
\vol 1
\issue 2
\pages 233--246
\mathnet{http://mi.mathnet.ru/nd201}


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  • http://mi.mathnet.ru/eng/nd/v1/i2/p233

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. N. Kulik, A. V. Tur, V. V. Yanovskii, “Evolyutsiya tochechnogo vikhrya dipolnogo tipa v krugovoi oblasti”, Nelineinaya dinam., 9:4 (2013), 659–670  mathnet
    2. 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  crossref  isi
    3. 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  mathnet  crossref
  • Нелинейная динамика
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