Geodesic
The dynamics of three vortex sources
Russian journal of nonlinear dynamics, Tome 10 (2014) no. 3, pp. 319-327.

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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.
Keywords: integrability, shape sphere, reduction, homothetic configurations.
Mots-clés : vortex sources 
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Ivan A. Bizyaev; Alexey V. Borisov; Ivan S. Mamaev. The dynamics of three vortex sources. Russian journal of nonlinear dynamics, Tome 10 (2014) no. 3, pp. 319-327. http://geodesic.mathdoc.fr/item/ND_2014_10_3_a5/

[1] Borisov A. V., Mamaev I. S., Matematicheskie metody dinamiki vikhrevykh struktur, Institut kompyuternykh issledovanii, M.–Izhevsk, 2005, 368 pp.

[2] Fridman A. A., Polubarinova P. Ya., “O peremeschayuschikhsya osobennostyakh ploskogo dvizheniya neszhimaemoi zhidkosti”, Geofiz. sb., 5:2 (1928), 9–23

[3] Bogomolov V. A., “Dvizhenie idealnoi zhidkosti postoyannoi plotnosti pri nalichii stokov”, Izv. AN SSSR. Mekhanika zhidkosti i gaza, 1976, no. 4, 21–27

[4] Sedov Yu. B., “Vzaimodeistvie spiralnykh vikhrei”, Izv. RAN. Mekhanika zhidkosti i gaza, 1995, no. 4, 183–185

[5] Jones S. W., Aref H., “Chaotic advection in pulsed source-sink systems”, Phys. Fluids, 31:3 (1988), 469–485 | DOI | MR

[6] Stremler M. A., Haselton F. R., Aref H., “Designing for chaos: Applications of chaotic advection at the microscale”, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 362:1818 (2004), 1019–1036 | DOI | MR

[7] Novikov A. E., Novikov E. A., “Vortex-sink dynamics”, Phys. Rev. E, 54:4 (1996), 3681–3686 | DOI

[8] Noguchi T., Yukimoto S., Kimura R., Niino H., “Structure and instability of a sink vortex”, Proc. PSFVIP-4 (Chamonix, France, 2003)

[9] Kozlov V. V., “Teorema Eilera–Yakobi–Li ob integriruemosti”, Nelineinaya dinamika, 9:2 (2013), 229–245

[10] Chenciner A., Montgomery R., “A remarkable periodic solution of the three-body problem in the case of equal masses”, Ann. of Math. (2), 152:2 (2000), 881–901 ; К. Симо, С. Смейл, А. Шенсине и др., Современные проблемы хаоса и нелинейности, Сб. ст., НИЦ «РХД», Институт компьютерных исследований, М.–Ижевск, 2002, 183–205 | DOI | MR | Zbl

[11] Borisov A. V., Mamaev I. S., “On the problem of motion vortex sources on a plane”, Regul. Chaotic Dyn., 11:4 (2006), 455–466 | DOI | MR | Zbl