Regular and Chaotic Dynamics

, Volume 19, Issue 6, pp 694–701 | Cite as

The dynamics of three vortex sources

  • Ivan A. Bizyaev
  • Alexey V. Borisov
  • Ivan S. Mamaev


In this paper, the integrability of the equations of a system of three vortex sources is shown. A reduced system describing, up to similarity, the evolution of the system’s configurations is obtained. Possible phase portraits and various relative equilibria of the system are presented.


integrability vortex sources shape sphere reduction homothetic configurations 

MSC2010 numbers

37N05 76M23 


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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  • Ivan A. Bizyaev
    • 1
  • Alexey V. Borisov
    • 1
    • 2
  • Ivan S. Mamaev
    • 1
    • 3
  1. 1.Udmurt State UniversityIzhevskRussia
  2. 2.Institute of Mathematics and Mechanics of the Ural Branch of RASEkaterinburgRussia
  3. 3.Moscow Institute of Physics and TechnologyDolgoprudnyiRussia

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