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., 2016, Volume 21, Issue 1, Pages 1–17 (Mi rcd64)  

This article is cited in 4 scientific papers (total in 4 papers)

Topological Analysis Corresponding to the Borisov–Mamaev–Sokolov Integrable System on the Lie Algebra $so(4)$

Rasoul Akbarzadeh

Department of Fundamental Sciences, 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 is a Hamiltonian system with two degrees of freedom, where both the Hamiltonian and the additional integral are homogenous polynomials of degrees 2 and 4, respectively. In this paper, the topology of isoenergy surfaces for the integrable case under consideration on the Lie algebra $so(4)$ and the critical points of the Hamiltonian under consideration for different values of parameters are described and the bifurcation values of the Hamiltonian are constructed. Also, a description of bifurcation complexes and typical forms of the bifurcation diagram of the system are presented.

Keywords: topology, integrable Hamiltonian systems, isoenergy surfaces, critical set, bifurcation diagram, bifurcation complex, periodic trajectory

DOI: https://doi.org/10.1134/S1560354716010019

References: PDF file   HTML file

Bibliographic databases:

MSC: 37Jxx, 70H06, 70E50, 70G40, 70H14
Received: 17.09.2015
Accepted:20.12.2015
Language:

Citation: 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

Citation in format AMSBIB
\Bibitem{Akb16}
\by Rasoul Akbarzadeh
\paper Topological Analysis Corresponding to the Borisov–Mamaev–Sokolov Integrable System on the Lie Algebra $so(4)$
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 1
\pages 1--17
\mathnet{http://mi.mathnet.ru/rcd64}
\crossref{https://doi.org/10.1134/S1560354716010019}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3457073}
\zmath{https://zbmath.org/?q=an:06580139}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000373028300001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84957586219}


Linking options:
  • http://mi.mathnet.ru/eng/rcd64
  • http://mi.mathnet.ru/eng/rcd/v21/i1/p1

    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. 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
    2. 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
    3. 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
    4. 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:166
    References:20

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