Аннотация:
In the reduced phase space by rotation, we prove the existence of periodic
orbits of the nn-vortex problem emanating from a relative equilibrium
formed by nn unit vortices at the vertices of a regular polygon, both in
the plane and at a fixed latitude when the ideal fluid moves on the
surface of a sphere. In the case of a plane we also prove the existence of
such periodic orbits in the (n+1)(n+1)-vortex problem, where an additional
central vortex of intensity κκ is added to the ring of the polygonal
configuration.
Ключевые слова:
point vortices; relative equilibria; periodic orbits; Lyapunov center theorem.
Поступила в редакцию: 01.10.2012 Принята в печать: 02.02.2014
Образец цитирования:
Adecarlos C. Carvalho, Hildeberto E. Cabral, “Lyapunov Orbits in the nn-Vortex Problem”, Regul. Chaotic Dyn., 19:3 (2014), 348–362
\RBibitem{CarCab14}
\by Adecarlos~C.~Carvalho, Hildeberto~E.~Cabral
\paper Lyapunov Orbits in the $n$-Vortex Problem
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 3
\pages 348--362
\mathnet{http://mi.mathnet.ru/rcd158}
\crossref{https://doi.org/10.1134/S156035471403006X}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3215694}
\zmath{https://zbmath.org/?q=an:1308.76048}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000337051600006}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd158
https://www.mathnet.ru/rus/rcd/v19/i3/p348
Эта публикация цитируется в следующих 6 статьяx:
Wang Q., “The N-Vortex Problem on a Riemann Sphere”, Commun. Math. Phys., 385:1 (2021), 565–593
C. Garcia-Azpeitia, “Relative periodic solutions of the n-vortex problem on the sphere”, J. Geom. Mech., 11:3 (2019), 427–438
Q. Wang, “Relative periodic solutions of the n-vortex problem via the variational method”, Arch. Ration. Mech. Anal., 231:3 (2019), 1401–1425
Renato C. Calleja, Eusebius J. Doedel, Carlos García-Azpeitia, “Choreographies in the n-vortex Problem”, Regul. Chaotic Dyn., 23:5 (2018), 595–612
С. В. Соколов, “К вопросу о движении в идеальной жидкости кругового цилиндра и вихревой пары в поле тяжести”, Докл. РАН, 470:4 (2016), 393–396; S. V. Sokolov, “On the problem of falling motion of a circular cylinder and a vortex pair in a perfect fluid”, Dokl. Math., 94:2 (2016), 594–597
Adecarlos C. Carvalho, Hildeberto E. Cabral, “Lyapunov Orbits in the $n$-Vortex Problem on the Sphere”, Regul. Chaotic Dyn., 20:3 (2015), 234–246
Цитирование в формате AMSBIB
Обратная связь: