RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
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., 2015, Volume 20, Issue 3, Pages 317–344 (Mi rcd46)  

This article is cited in 5 scientific papers (total in 5 papers)

The Topology of Liouville Foliation for the Borisov–Mamaev–Sokolov Integrable Case on the Lie Algebra $so(4)$

Rasoul Akbarzadeh, Ghorbanali Haghighatdoost

Azarbaijan Shahid Madani University, 35 Km Tabriz-Maragheh Road, Tabriz, Iran

Abstract: In 2001, A.V. Borisov, I.S. Mamaev, and V.V. Sokolov discovered a new integrable case on the Lie algebra $so(4)$. This system coincides with the Poincaré equations on the Lie algebra $so(4)$, which describe the motion of a body with cavities filled with an incompressible vortex fluid. Moreover, the Poincaré equations describe the motion of a four-dimensional gyroscope. In this paper topological properties of this system are studied. In particular, for the system under consideration the bifurcation diagrams of the momentum mapping are constructed and all Fomenko invariants are calculated. Thereby, a classification of isoenergy surfaces for this system up to the rough Liouville equivalence is obtained.

Keywords: integrable Hamiltonian systems, isoenergy surfaces, Kirchhoff equations, Liouville foliation, bifurcation diagram, Borisov–Mamaev–Sokolov case, topological invariant

DOI: https://doi.org/10.1134/S1560354715030089

References: PDF file   HTML file

Bibliographic databases:

MSC: 37J35, 70H06
Received: 06.03.2015
Language:

Citation: Rasoul Akbarzadeh, Ghorbanali Haghighatdoost, “The Topology of Liouville Foliation for the Borisov–Mamaev–Sokolov Integrable Case on the Lie Algebra $so(4)$”, Regul. Chaotic Dyn., 20:3 (2015), 317–344

Citation in format AMSBIB
\Bibitem{AkbHag15}
\by Rasoul Akbarzadeh, Ghorbanali Haghighatdoost
\paper The Topology of Liouville Foliation for the Borisov–Mamaev–Sokolov Integrable Case on the Lie Algebra $so(4)$
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 3
\pages 317--344
\mathnet{http://mi.mathnet.ru/rcd46}
\crossref{https://doi.org/10.1134/S1560354715030089}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3357279}
\zmath{https://zbmath.org/?q=an:06488660}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2015RCD....20..317A}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000356354200008}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84934897371}


Linking options:
  • http://mi.mathnet.ru/eng/rcd46
  • http://mi.mathnet.ru/eng/rcd/v20/i3/p317

    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

    This publication is cited in the following articles:
    1. Rasoul Akbarzadeh, “Topological Analysis Corresponding to the Borisov–Mamaev–Sokolov Integrable System on the Lie Algebra $so(4)$”, Regul. Chaotic Dyn., 21:1 (2016), 1–17  mathnet  crossref  mathscinet  zmath
    2. Pavel E. Ryabov, Andrej A. Oshemkov, Sergei V. Sokolov, “The Integrable Case of Adler – van Moerbeke. Discriminant Set and Bifurcation Diagram”, Regul. Chaotic Dyn., 21:5 (2016), 581–592  mathnet  crossref  mathscinet  zmath
    3. A. A. Oshemkov, P. E. Ryabov, S. V. Sokolov, “Explicit determination of certain periodic motions of a generalized two-field gyrostat”, Russ. J. Math. Phys., 24:4 (2017), 517–525  crossref  mathscinet  zmath  isi  scopus
    4. P. E. Ryabov, “Explicit integration of the system of invariant relations for the case of M. Adler and P. van Moerbeke”, Dokl. Math., 95:1 (2017), 17–20  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    5. R. Akbarzadeh, “The topology of isoenergetic surfaces for the Borisov–Mamaev–Sokolov integrable case on the Lie algebra $so(3,1)$”, Theoret. and Math. Phys., 197:3 (2018), 1727–1736  mathnet  crossref  crossref  adsnasa  isi  elib
  • Number of views:
    This page:270
    References:24

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