RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2009, Volume 85, Issue 4, Pages 524–537 (Mi mz4118)  

Integral Formula for a Generalized Sato–Levine Invariant in Magnetic Hydrodynamics

P. M. Akhmet'eva, O. V. Kunakovskayab

a Steklov Mathematical Institute, Russian Academy of Sciences
b Voronezh State University

Abstract: For a pair of divergence-free vector fields $\mathbf B$ and $\widetilde{\mathbf B}$ respectively localized in two oriented tubes $U$ and $\widetilde U$ in $\mathbb R^3$, we propose a fourth-order integral $W$ and describe the dependence between the integral $W$ and a higher topological invariant $\beta=\beta(l,\widetilde l)$ (namely, the generalized Sato–Levine invariant). The new integral is a generalization of the well-known integral, which was defined earlier for two tubes with zero linking number.

Keywords: topological invariant, Sato–Levine invariant, oriented magnetic tube, linking number, magnetic hydrodynamics, Lie derivative, Massey product, gradient field

DOI: https://doi.org/10.4213/mzm4118

Full text: PDF file (538 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2009, 85:4, 503–514

Bibliographic databases:

UDC: 517.958
Received: 10.10.2007
Revised: 21.04.2008

Citation: P. M. Akhmet'ev, O. V. Kunakovskaya, “Integral Formula for a Generalized Sato–Levine Invariant in Magnetic Hydrodynamics”, Mat. Zametki, 85:4 (2009), 524–537; Math. Notes, 85:4 (2009), 503–514

Citation in format AMSBIB
\Bibitem{AkhKun09}
\by P.~M.~Akhmet'ev, O.~V.~Kunakovskaya
\paper Integral Formula for a Generalized Sato--Levine Invariant in Magnetic Hydrodynamics
\jour Mat. Zametki
\yr 2009
\vol 85
\issue 4
\pages 524--537
\mathnet{http://mi.mathnet.ru/mz4118}
\crossref{https://doi.org/10.4213/mzm4118}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2549415}
\zmath{https://zbmath.org/?q=an:1190.53071}
\transl
\jour Math. Notes
\yr 2009
\vol 85
\issue 4
\pages 503--514
\crossref{https://doi.org/10.1134/S0001434609030225}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000266561100022}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-69949145996}


Linking options:
  • http://mi.mathnet.ru/eng/mz4118
  • https://doi.org/10.4213/mzm4118
  • http://mi.mathnet.ru/eng/mz/v85/i4/p524

    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
  • Математические заметки Mathematical Notes
    Number of views:
    This page:344
    Full text:105
    References:61
    First page:15

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020