A. V. Borisov, V. G. Lebedev, “Dynamics of Three Vortices on a Plane and a Sphere — III. Noncompact Case. Problems of Collaps and Scattering”, Regul. Chaotic Dyn., 3:4 (1998), 74

Loading [MathJax]/jax/output/CommonHTML/jax.js

Regular and Chaotic Dynamics

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Regular and Chaotic Dynamics, 1998, Volume 3, Issue 4, Pages 74–86
DOI: https://doi.org/10.1070/RD1998v003n04ABEH000094 (Mi rcd963)

This article is cited in 16 scientific papers (total in 16 papers)

Dynamics of Three Vortices on a Plane and a Sphere — III. Noncompact Case. Problems of Collaps and Scattering

A. V. Borisov^a, V. G. Lebedev^b

^a Faculty of Mechanics an d Mathematics, Department of Theoretical Mechanics, Moscow State University, Vorob'ievy gory, Moscow, Russia , 119899
^b Physical Faculty, Department of Theoretical Physics, Udmurt State University, Universitetskaya , 1, Izhevsk, 426034

Citations (16)

DOI: https://doi.org/10.1070/RD1998v003n04ABEH000094

Abstract: In this article we considered the integrable problems of three vortices on a plane and sphere for noncompact case. We investigated explicitly the problems of a collapse and scattering of vortices and obtained the conditions of realization. We completed the bifurcation analysis and investigated the dependence of stability in linear approximation and frequency of rotation in relative coordinates for collinear and Thomson's configurations from value of a full moment and indicated the geometric interpretation for characteristic situations. We constructed a phase portrait and geometric projection for an integrable configuration of four vortices on a plane.

Received: 25.10.1998

Bibliographic databases:

Document Type: Article

MSC: 76C05

Language: English

Citation: A. V. Borisov, V. G. Lebedev, “Dynamics of Three Vortices on a Plane and a Sphere — III. Noncompact Case. Problems of Collaps and Scattering”, Regul. Chaotic Dyn., 3:4 (1998), 74–86

Citation in format AMSBIB

\Bibitem{BorLeb98}

\by A. V. Borisov, V. G. Lebedev

\paper Dynamics of Three Vortices on a Plane and a Sphere — III. Noncompact Case. Problems of Collaps and Scattering

\jour Regul. Chaotic Dyn.

\yr 1998

\vol 3

\issue 4

\pages 74--86

\mathnet{http://mi.mathnet.ru/rcd963}

\crossref{https://doi.org/10.1070/RD1998v003n04ABEH000094}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1704984}

\zmath{https://zbmath.org/?q=an:0958.76013}

Linking options:

https://www.mathnet.ru/eng/rcd963

https://www.mathnet.ru/eng/rcd/v3/i4/p74

This publication is cited in the following 16 articles:

Makarov V.G., “Group Scattering of Point Vortices on An Unbounded Plane”, J. Fluid Mech., 911 (2021), A24
Alexander A. Kilin, Lizaveta M. Artemova, “Integrability and Chaos in Vortex Lattice Dynamics”, Regul. Chaotic Dyn., 24:1 (2019), 101–113
Björn Gebhard, Rafael Ortega, “Stability of Periodic Solutions of the $N$ -vortex Problem in General Domains”, Regul. Chaotic Dyn., 24:6 (2019), 649–670
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
E. V. Vetchanin, A. O. Kazakov, “Bifurcations and chaos in the dynamics of two point vortices in an acoustic wave”, Int. J. Bifurcation Chaos Appl. Sci. Eng., 26:4 (2016), 1650063–13
Stefanella Boatto, Jair Koiller, Fields Institute Communications, 73, Geometry, Mechanics, and Dynamics, 2015, 185
Mikhail A. Sokolovskiy, Jacques Verron, Atmospheric and Oceanographic Sciences Library, 47, Dynamics of Vortex Structures in a Stratified Rotating Fluid, 2014, 1
Mikhail A. Sokolovskiy, Jacques Verron, Atmospheric and Oceanographic Sciences Library, 47, Dynamics of Vortex Structures in a Stratified Rotating Fluid, 2014, 37
Mikhail A. Sokolovskiy, Jacques Verron, Atmospheric and Oceanographic Sciences Library, 47, Dynamics of Vortex Structures in a Stratified Rotating Fluid, 2014, 317
Mikhail A. Sokolovskiy, Jacques Verron, Atmospheric and Oceanographic Sciences Library, 47, Dynamics of Vortex Structures in a Stratified Rotating Fluid, 2014, 179
K. N. Kulik, A. V. Tur, V. V. Yanovskii, “Evolyutsiya tochechnogo vikhrya dipolnogo tipa v krugovoi oblasti”, Nelineinaya dinam., 9:4 (2013), 659–670
A. I. Gudimenko, A. D. Zakharenko, “Kachestvennyi analiz otnositelnogo dvizheniya trekh vikhrei”, Nelineinaya dinam., 6:2 (2010), 307–326
V. V. Meleshko, P. K. Newton, V. V. Ostrovs'kyi, “Stability of the configurations of point vortices on a sphere”, J Math Sci, 171:5 (2010), 603
A. V. Borisov, I. S. Mamaev, S. M. Ramodanov, “Coupled motion of a rigid body and point vortices on a two-dimensional spherical surface”, Regul. Chaotic Dyn., 15:4 (2010), 440–461
Yasuaki Hiraoka, “Topological regularizations of the triple collision singularity in the 3-vortex problem”, Nonlinearity, 21:2 (2008), 361
Paul K. Newton, Shane D. Ross, “Chaotic advection in the restricted four-vortex problem on a sphere”, Physica D: Nonlinear Phenomena, 223:1 (2006), 36

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	120

Что такое QR-код?

Registration to the website

Logotypes