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. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb., 2011, Volume 202, Number 5, Pages 127–160 (Mi msb7823)  

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

Topological features of the Sokolov integrable case on the Lie algebra $\mathrm{e}(3)$

D. V. Novikov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The Sokolov integrable case on $\mathrm{e}(3)^{\star}$ is investigated. This is a Hamiltonian system with $2$ degrees of freedom in which the Hamiltonian and the additional integral are homogeneous polynomials having degree $2$ and $4$, respectively. This system is of interest because connected joint level surfaces of the Hamiltonian and the additional integral are noncompact. The critical points of the moment map and their indices are found, the bifurcation diagram is constructed and the Liouville foliation of the system is described. The Hamiltonian vector fields corresponding to the Hamiltonian and the additional integral are proved to be complete.
Bibliography: 22 titles.

Keywords: integrable Hamiltonian systems, completeness of vector fields, bifurcation diagram, moment map, noncompact singularities.

DOI: https://doi.org/10.4213/sm7823

Full text: PDF file (720 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2011, 202:5, 749–781

Bibliographic databases:

UDC: 517.938.5
MSC: Primary 37J35; Secondary 70E40
Received: 23.11.2010

Citation: D. V. Novikov, “Topological features of the Sokolov integrable case on the Lie algebra $\mathrm{e}(3)$”, Mat. Sb., 202:5 (2011), 127–160; Sb. Math., 202:5 (2011), 749–781

Citation in format AMSBIB
\Bibitem{Nov11}
\by D.~V.~Novikov
\paper Topological features of the Sokolov integrable case on the Lie algebra $\mathrm{e}(3)$
\jour Mat. Sb.
\yr 2011
\vol 202
\issue 5
\pages 127--160
\mathnet{http://mi.mathnet.ru/msb7823}
\crossref{https://doi.org/10.4213/sm7823}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2841522}
\zmath{https://zbmath.org/?q=an:1246.37081}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2011SbMat.202..749N}
\elib{https://elibrary.ru/item.asp?id=19066281}
\transl
\jour Sb. Math.
\yr 2011
\vol 202
\issue 5
\pages 749--781
\crossref{https://doi.org/10.1070/SM2011v202n05ABEH004165}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000294703200008}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80051695511}


Linking options:
  • http://mi.mathnet.ru/eng/msb7823
  • https://doi.org/10.4213/sm7823
  • http://mi.mathnet.ru/eng/msb/v202/i5/p127

    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. Novikov D.V., “The topology of isoenergy surfaces for the Sokolov integrable case on the Lie algebra so(3,1)”, Moscow Univ. Math. Bull., 66:4 (2011), 181–184  mathnet  crossref  mathscinet  zmath  elib  elib  scopus
    2. D. V. Novikov, “Topological features of the Sokolov integrable case on the Lie algebra $\mathrm{so}(3,1)$”, Sb. Math., 205:8 (2014), 1107–1132  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. D. A. Fedoseev, A. T. Fomenko, “Nekompaktnye osobennosti integriruemykh dinamicheskikh sistem”, Fundament. i prikl. matem., 21:6 (2016), 217–243  mathnet
    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
    5. S. S. Nikolaenko, “Topological classification of Hamiltonian systems on two-dimensional noncompact manifolds”, Sb. Math., 211:8 (2020), 1127–1158  mathnet  crossref  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:401
    Full text:115
    References:42
    First page:39

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