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@article{ND_2014_10_3_a6,
author = {Evgeny V. Vetchanin and Alexey O. Kazakov},
title = {Bifurcations and chaos in the problem of the motion of two point vortices in an acoustic wave},
journal = {Russian journal of nonlinear dynamics},
pages = {329--343},
publisher = {mathdoc},
volume = {10},
number = {3},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ND_2014_10_3_a6/}
}
TY - JOUR AU - Evgeny V. Vetchanin AU - Alexey O. Kazakov TI - Bifurcations and chaos in the problem of the motion of two point vortices in an acoustic wave JO - Russian journal of nonlinear dynamics PY - 2014 SP - 329 EP - 343 VL - 10 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ND_2014_10_3_a6/ LA - ru ID - ND_2014_10_3_a6 ER -
%0 Journal Article %A Evgeny V. Vetchanin %A Alexey O. Kazakov %T Bifurcations and chaos in the problem of the motion of two point vortices in an acoustic wave %J Russian journal of nonlinear dynamics %D 2014 %P 329-343 %V 10 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/ND_2014_10_3_a6/ %G ru %F ND_2014_10_3_a6
Evgeny V. Vetchanin; Alexey O. Kazakov. Bifurcations and chaos in the problem of the motion of two point vortices in an acoustic wave. Russian journal of nonlinear dynamics, Tome 10 (2014) no. 3, pp. 329-343. http://geodesic.mathdoc.fr/item/ND_2014_10_3_a6/
[1] Gelmgolts G., “Ob integralakh uravnenii gidrodinamiki, sootvetstvuyuschikh vikhrevym dvizheniyam”, Nelineinaya dinamika, 2:4 (2006), 473–507
[2] Kirkhgof G., Mekhanika. Lektsii po matematicheskoi fizike, AN SSSR, M., 1962, 404 pp.
[3] Puankare A., Teoriya vikhrei, NITs «Regulyarnaya i khaoticheskaya dinamika», M.–Izhevsk, 2000, 160 pp.
[4] Tsermelo E., “Gidrodinamicheskie issledovaniya vikhrevykh dvizhenii na poverkhnosti sfery”, Nelineinaya dinamika, 3:1 (2007), 81–110
[5] Bogomolov V. A., “Dinamika zavikhrennosti na sfere”, Izv. AN SSSR. Mekhanika zhidkosti i gaza, 1977, no. 6, 57–65
[6] Bogomolov V. A., “O dvumernoi gidrodinamike na sfere”, Izv. AN SSSR. Fizika atmosfery i okeana, 15:1 (1979), 29–35
[7] Khanin K. M., “Quasi-periodic motions of vortex systems”, Phys. D, 4:2 (1982), 261–269 | DOI | MR | Zbl
[8] Kidambi R., Newton P. K., “Motion of three point vortices on a sphere”, Phys. D, 116:1 (1998), 143–175 | DOI | MR | Zbl
[9] Borisov A. V., Mamaev I. S., Kilin A. A., “Absolute and relative choreographies in the problem of point vortices moving on a plane”, Regul. Chaotic Dyn., 9:2 (2004), 101–112 | DOI | MR
[10] Borisov A. V., Mamaev I. S., Kilin A. A., “New periodic solutions for three or four identical vortices on a plane and a sphere”, Supplement Volume 2005 of DCDS-B devoted to the 5th AIMS International Conference on Dynamical Systems and Differential Equations (Pomona, California, USA, June 2004), 110–120 | MR | Zbl
[11] Brutyan M. A., Krapivskii P. L., “Dvizhenie sistemy vikhrevykh kolets v neszhimaemoi zhidkosti”, PMM, 48:3 (1984), 503–506
[12] Boyarintsev V. I., Levchenko E. S., Savin A. S., “O dvizhenii dvukh vikhrevykh kolets”, Izv. AN SSSR. Mekhanika zhidkosti i gaza, 1985, no. 5, 176–177
[13] Huang Y., Schorghofer N., Ching E. S. C., “Two vortex rings produce chaos”, Europhys. Lett., 52:4 (2000), 399–405 | DOI
[14] Blackmore D., Brons M., Goullet A., “A coaxial vortex ring model for vortex breakdown”, Phys. D, 237:22 (2008), 2817–2844 | DOI | MR | Zbl
[15] Borisov A. V., Kilin A. A., Mamaev I. S., “Dinamika vikhrevykh kolets: Chekharda, khoreografii i problema ustoichivosti”, Nelineinaya dinamika, 8:1 (2012), 113–147 | MR
[16] Borisov A. V., Kilin A. A., Mamaev I. S., Tenenev V. A., “The dynamics of vortex rings: Leapfrogging in an ideal and viscous fluid”, Fluid Dyn. Res., 46:3 (2014), 31415–31430 | DOI | MR
[17] Borisov A. V., Mamaev I. S., Matematicheskie metody dinamiki vikhrevykh struktur, Institut kompyuternykh issledovanii, M.–Izhevsk, 2005, 368 pp.
[18] Ryzhov E. A., “On changing the size of the atmosphere of a vortex pair embedded in a periodic external shear flow”, Phys. Lett. A, 375:44 (2011), 3884–3889 | DOI | Zbl
[19] Ryzhov E. A., Koshel K. V., “Dynamics of a vortex pair interacting with a fixed point vortex”, Europhys. Lett., 102:4 (2013), 44004, 6 pp. | DOI
[20] Lighthill M. J., “On sound generated aerodynamically. 1: General theory”, Proc. Roy. Soc. London. Ser. A, 211 (1952), 564–587 | DOI | MR | Zbl
[21] Liepmann H. W., On the acoustic radiation from boundary layers and jets, Technical report, , 1954 http://authors.library.caltech.edu/12113/1/HWLiepmann.pdf
[22] Powell A., “Theory of vortex sound”, J. Acoust. Soc. Am., 36:1 (1964), 177–195 | DOI | MR
[23] Hardin J. C., Mason J. P., “Broadband noise generation by a vortex model of cavity flow”, AIAA J., 15:5 (1977), 632–637 | DOI | Zbl
[24] Yates J. E., Interaction with and production of sound by vortex flows, AIAA Paper 77-1352, 1977
[25] Gonchar V. Yu., Ostapchuk P. N., Tur A. V., Yanovsky V. V., “Dynamics and stochasticity in a reversible system describing interaction of point vortices with a potential wave”, Phys. Lett. A, 152:5–6 (1991), 287–292 | DOI | MR
[26] Yates J. E., Sandri G., “Bernoulli enthalpy: A fundamental concept in the theory of sound”, 2nd Aero-Acoustics Conf. (Hampton, Va., Mar. 24–26, 1975), 12 pp.
[27] Quispel G. R. W., Roberts J. A. G., “Conservative and dissipative behaviour in reversible dynamical systems”, Phys. Lett. A, 135:6 (1989), 337–342 | DOI | MR
[28] Borisov A. V., Mamaev I. S., Kilin A. A., “Reduction and chaotic behavior of point vortices on a plane and a sphere”, Supplement Volume 2005 of DCDS-B devoted to the 5th AIMS International Conference on Dynamical Systems and Differential Equations, Pomona, California, USA, June 2004, 100–109 | MR | Zbl
[29] Kochin N. E., Kibel I. A., Roze N. V., Teoreticheskaya gidromekhanika, v. 1, Fizmatlit, M., 1963, 584 pp.
[30] Borisov A. V., Kilin A. A., Mamaev I. S., “Perekhod k khaosu v dinamike chetyrekh tochechnykh vikhrei na ploskosti”, Dokl. RAN, 408:1 (2006), 49–54 | MR | Zbl
[31] Bolgarskii A. V., Termodinamika i teploperedacha, 2-e izd., pererab. i dop., Vyssh. shkola, M., 1975, 495 pp.
[32] Gelfer Ya. M., Istoriya i metodologiya termodinamiki i statisticheskoi fiziki, 2-e izd., pererab. i dop., Vyssh. shkola, M., 1981, 536 pp.
[33] Lerman L. M., Turaev D. V., “O bifurkatsiyakh poteri simmetrii v obratimykh sistemakh”, Nelineinaya dinamika, 8:2 (2012), 323–343
[34] Post T., Capel H. W., Quispel G. R. W., van der Weele J. P., “Bifurcations in two-dimensional reversible maps”, Phys. A, 164:3 (1990), 625–662 | DOI | MR | Zbl
[35] Borisov A. V., Mamaev I. S., Bizyaev I. A., “Ierarkhiya dinamiki pri kachenii tverdogo tela bez proskalzyvaniya i vercheniya po ploskosti i sfere”, Nelineinaya dinamika, 9:2 (2013), 141–202
[36] Borisov A. V., Mamaev I. S., “Strannye attraktory v dinamike keltskikh kamnei”, UFN, 173:4 (2003), 407–418 | DOI
[37] Kuznetsov S. P., Dinamicheskii khaos, 2-e izd., Fizmatlit, M., 2006, 356 pp.
[38] Kuznetsov S. P., Zhalnin A. Yu., Sataev I. R., Sedova Yu. V., “Fenomeny nelineinoi dinamiki dissipativnykh sistem v negolonomnoi mekhanike «keltskogo kamnya»”, Nelineinaya dinamika, 8:4 (2012), 735–762
[39] Borisov A. V., Kazakov A. O., Kuznetsov S. P., “Nelineinaya dinamika keltskogo kamnya: negolonomnaya model”, UFN, 184:5 (2014), 493–500 | DOI
[40] Borisov A. V., Mamaev I. S., “Dinamika sanei Chaplygina”, PMM, 73:2 (2009), 219–225 | MR | Zbl