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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2011, Number 4, Pages 62–65 (Mi vmumm708)  

This article is cited in 2 scientific papers (total in 2 papers)

Short notes

The topology of isoenergy surfaces for the Sokolov integrable case on the Lie algebra $\operatorname{so}(3,1)$

D. V. Novikov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Sokolov's integrable case on $\operatorname{so}(3,1)$ is studied. This is a Hamiltonian system with two degrees of freedom where both the hamiltonian and additional integral are homogeneous polynomials of degrees $2$ and $4$, respectively. The topology of isoenergy surfaces is described for different values of parameters.

Key words: integrable Hamiltonian systems, bifurcation diagram, isoenergy surface.

Funding Agency Grant Number
Russian Foundation for Basic Research 10-01-00748
Ministry of Education and Science of the Russian Federation НШ-3224.2010.1
02.740.11.5213
14.740.11.0794
РНП-2.1.1.3704


Full text: PDF file (313 kB)

Bibliographic databases:
UDC: 517.938.5
Received: 24.12.2010

Citation: D. V. Novikov, “The topology of isoenergy surfaces for the Sokolov integrable case on the Lie algebra $\operatorname{so}(3,1)$”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2011, no. 4, 62–65

Citation in format AMSBIB
\Bibitem{Nov11}
\by D.~V.~Novikov
\paper The topology of isoenergy surfaces for the Sokolov integrable case on the Lie algebra $\operatorname{so}(3,1)$
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2011
\issue 4
\pages 62--65
\mathnet{http://mi.mathnet.ru/vmumm708}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2919098}
\zmath{https://zbmath.org/?q=an:1304.37038}


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    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. 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
    2. 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
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