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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, Issue 4, Pages 40–59 (Mi vuu295)  

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

MATHEMATICS

Smale–Fomenko diagrams and rough topological invariants of the Kowalevski–Yehia case

M. P. Kharlamova, P. E. Ryabovb

a Russian Presidential Academy of National Economy and Public Administration, Volgograd Branch, Volgograd, Russia
b Financial University under the Government of the Russian Federation, Moscow, Russia

Abstract: We present the complete analytical classification of the atoms arising at the critical points of rank 1 of the Kowalevski–Yehia gyrostat. To classify the Smale–Fomenko diagrams, all separating values of the gyrostatic momentum are found. We present a kind of constructor of the Fomenko graphs; its application gives the complete description of the rough topology of this integrable case. It is proved that there exists exactly nine groups of identical molecules (not considering the marks). These groups contain 22 stable types of graphs and 6 unstable ones with respect to the number of critical circles on the critical levels.

Keywords: gyrostat, Kowalevski–Yehia case, diagrams, topological invariants.

Full text: PDF file (1785 kB)
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UDC: 517.938.5+531.38
MSC: 70E17, 70G40
Received: 01.11.2011

Citation: M. P. Kharlamov, P. E. Ryabov, “Smale–Fomenko diagrams and rough topological invariants of the Kowalevski–Yehia case”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 4, 40–59

Citation in format AMSBIB
\Bibitem{KhaRya11}
\by M.~P.~Kharlamov, P.~E.~Ryabov
\paper Smale--Fomenko diagrams and rough topological invariants of the Kowalevski--Yehia case
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2011
\issue 4
\pages 40--59
\mathnet{http://mi.mathnet.ru/vuu295}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Slavina N.S., “Classification of the Family of Kovalevskaya-Yehia Systems Up to Liouville Equivalence”, Dokl. Math., 88:2 (2013), 537–540  crossref  mathscinet  zmath  isi  elib
    2. N. S. Slavina, “Topological classification of systems of Kovalevskaya-Yehia type”, Sb. Math., 205:1 (2014), 101–155  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. P. E. Ryabov, A. Yu. Savushkin, “Fazovaya topologiya volchka Kovalevskoi – Sokolova”, Nelineinaya dinam., 11:2 (2015), 287–317  mathnet
    4. Mikhail P. Kharlamov, Pavel E. Ryabov, Alexander Yu. Savushkin, “Topological Atlas of the Kowalevski–Sokolov Top”, Regul. Chaotic Dyn., 21:1 (2016), 24–65  mathnet  crossref  mathscinet  zmath
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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