A. V. Borisov, A. E. Pavlov, “Dynamics and statics of vortices on a plane and a sphere – I”, Regul. Chaotic Dyn., 3:1 (1998), 28

Regular and Chaotic Dynamics

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ЖУРНАЛЫ ПЕРСОНАЛИИ ОРГАНИЗАЦИИ КОНФЕРЕНЦИИ СЕМИНАРЫ ВИДЕОТЕКА ПАКЕТ AMSBIB

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Regular and Chaotic Dynamics, 1998, том 3, выпуск 1, страницы 28–38
DOI: https://doi.org/10.1070/RD1998v003n01ABEH000059 (Mi rcd926)

Эта публикация цитируется в 36 научных статьях (всего в 37 статьях)

Dynamics and statics of vortices on a plane and a sphere – I

A. V. Borisov^a, A. E. Pavlov^b

^a Faculty of Mechanics and Mathematics, Department of Theoretical Mechanics, Moscow State University, Vorob'ievy gory, 119899 Moscow, Russia
^b Laboratory of Nonlinear Dynamics and Synergetics, Udmurt State University, Universitetskaya Str. 1, 426034. Izhevsk, Russia

Список цитирования (37)

DOI: https://doi.org/10.1070/RD1998v003n01ABEH000059

Аннотация: In the present paper a description of a problem of point vortices on a plane and a sphere in the "internal" variables is discussed. The hamiltonian equations of motion of vortices on a plane are built on the Lie–Poisson algebras, and in the case of vortices on a sphere on the quadratic Jacobi algebras. The last ones are obtained by deformation of the corresponding linear algebras. Some partial solutions of the systems of three and four vortices are considered. Stationary and static vortex configurations are found.

Поступила в редакцию: 01.10.1997

Реферативные базы данных:

Тип публикации: Статья

MSC: 76C05

Язык публикации: английский

Образец цитирования: A. V. Borisov, A. E. Pavlov, “Dynamics and statics of vortices on a plane and a sphere – I”, Regul. Chaotic Dyn., 3:1 (1998), 28–38

Цитирование в формате AMSBIB

\RBibitem{BorPav98}

\by A. V. Borisov, A. E. Pavlov

\paper Dynamics and statics of vortices on a plane and a sphere~--~I

\jour Regul. Chaotic Dyn.

\yr 1998

\vol 3

\issue 1

\pages 28--38

\mathnet{http://mi.mathnet.ru/rcd926}

\crossref{https://doi.org/10.1070/RD1998v003n01ABEH000059}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1652160}

\zmath{https://zbmath.org/?q=an:0934.76014}

Образцы ссылок на эту страницу:

https://www.mathnet.ru/rus/rcd926

https://www.mathnet.ru/rus/rcd/v3/i1/p28

Эта публикация цитируется в следующих 37 статьяx:

K. Constantineau, C. García-Azpeitia, L. C. García-Naranjo, J.-P. Lessard, “Determination of Stable Branches of Relative Equilibria of the N-Vortex Problem on the Sphere”, Commun. Math. Phys., 406:2 (2025)
Tomoki Ohsawa, “Shape dynamics of N point vortices on the sphere”, Nonlinearity, 36:2 (2023), 1000
Carlos García-Azpeitia, Luis C. García-Naranjo, “Platonic Solids and Symmetric Solutions of the N-vortex Problem on the Sphere”, J Nonlinear Sci, 32:3 (2022)
С. В. Соколов, “Памяти Алексея Владимировича Борисова”, Компьютерные исследования и моделирование, 13:1 (2021), 9–14
M. A. Stremler, “Something Old, Something New: Three Point Vortices on the Plane”, Regul. Chaotic Dyn., 26:5 (2021), 482–504
Artemova E. Kilin A., “Nonlinear Stability of Regular Vortex Polygons in a Bose-Einstein Condensate”, Phys. Fluids, 33:12 (2021), 127105
Ohsawa T., “Symplectic Reduction and the Lie-Poisson Shape Dynamics of N Point Vortices on the Plane”, Nonlinearity, 32:10 (2019), 3820–3842
Wang Q., “Relative Periodic Solutions of the N-Vortex Problem Via the Variational Method”, Arch. Ration. Mech. Anal., 231:3 (2019), 1401–1425
Vikas S. Krishnamurthy, Mark A. Stremler, “Finite-time Collapse of Three Point Vortices in the Plane”, Regul. Chaotic Dyn., 23:5 (2018), 530–550
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
Vikas S. Krishnamurthy, Hassan Aref, Mark A. Stremler, “Evolving geometry of a vortex triangle”, Phys. Rev. Fluids, 3:2 (2018)
Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “The Spatial Problem of 2 Bodies on a Sphere. Reduction and Stochasticity”, Regul. Chaotic Dyn., 21:5 (2016), 556–580
Eugene A. Ryzhov, Konstantin V. Koshel, “Parametric Instability of a Many Point-vortex System in a Multi-layer Flow Under Linear Deformation”, Regul. Chaotic Dyn., 21:3 (2016), 254–266
Maria V. Demina, Nikolai A. Kudryashov, “Multi-particle Dynamical Systems and Polynomials”, Regul. Chaotic Dyn., 21:3 (2016), 351–366
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of Vortex Sources in a Deformation Flow”, Regul. Chaotic Dyn., 21:3 (2016), 367–376
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
Adecarlos C. Carvalho, Hildeberto E. Cabral, “Lyapunov Orbits in the $n$ -Vortex Problem on the Sphere”, Regul. Chaotic Dyn., 20:3 (2015), 234–246
Stefanella Boatto, Jair Koiller, Fields Institute Communications, 73, Geometry, Mechanics, and Dynamics, 2015, 185
А. В. Борисов, И. С. Мамаев, “Симметрии и редукция в неголономной механике”, Нелинейная динам., 11:4 (2015), 763–823
Alexey V. Borisov, Ivan S. Mamaev, “Symmetries and Reduction in Nonholonomic Mechanics”, Regul. Chaotic Dyn., 20:5 (2015), 553–604

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

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