RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
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


Regul. Chaotic Dyn., 2018, Volume 23, Issue 5, Pages 613–636 (Mi rcd349)  

Three Vortices in Spaces of Constant Curvature: Reduction, Poisson Geometry, and Stability

Alexey V. Borisova, Ivan S. Mamaevb, Ivan A. Bizyaeva

a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
b Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700 Russia

Abstract: This paper is concerned with the problem of three vortices on a sphere $S^2$ and the Lobachevsky plane $L^2$. After reduction, the problem reduces in both cases to investigating a Hamiltonian system with a degenerate quadratic Poisson bracket, which makes it possible to study it using the methods of Poisson geometry. This paper presents a topological classification of types of symplectic leaves depending on the values of Casimir functions and system parameters.

Keywords: Poisson geometry, point vortices, reduction, quadratic Poisson bracket, spaces of constant curvature, symplectic leaf, collinear configurations

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.2404.2017/4.6
5-100
Russian Foundation for Basic Research 17-01-00846-a
The work of A.V. Borisov (Sections 1 and 2) and I.A. Bizyaev (Section 4) was carried out within the framework of the state assignment to the Ministry of Education and Science of Russia (1.2404.2017/4.6). The work of I. S. Mamaev (Section 3) is carried out at MIPT under project 5-100 for state support for leading universities of the Russian Federation. Also this work is supported by the Russian Foundation for Basic Research (Project No. 17-01-00846-a).


DOI: https://doi.org/10.1134/S1560354718050106

References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 76M23, 37J05
Received: 02.08.2018
Accepted:04.09.2018
Language: English

Citation: 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

Citation in format AMSBIB
\Bibitem{BorMamBiz18}
\by Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev
\paper Three Vortices in Spaces of Constant Curvature: Reduction, Poisson Geometry, and Stability
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 5
\pages 613--636
\mathnet{http://mi.mathnet.ru/rcd349}
\crossref{https://doi.org/10.1134/S1560354718050106}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000447268600010}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85054652455}


Linking options:
  • http://mi.mathnet.ru/eng/rcd349
  • http://mi.mathnet.ru/eng/rcd/v23/i5/p613

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:20
    References:7

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019