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Mat. Sb., 2012, Volume 203, Number 1, Pages 31–60 (Mi msb7824)  

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

Classification of nondegenerate equilibria and degenerate 1-dimensional orbits of the Kovalevskaya-Yehia integrable system

N. S. Logacheva

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

Abstract: The paper is devoted to a topological analysis of the Kovalevskaya-Yehia integrable case in rigid body dynamics. It is proved that the integral has the Bott property on isoenergy surfaces of the system; the topology of the Liouville foliation in a neighbourhood of degenerate 1-dimensional orbits and equilibria (points of rank 0) is also described. In particular, marked loop molecules are constructed for degenerate 1-dimensional orbits, and a representation in the form of an almost direct product is found for nondegenerate singularities of rank 0.
Bibliography: 17 titles.

Keywords: moment map, Liouville foliation, nondegenerate equilibria, degenerate 1-dimensional orbits, loop molecules.

DOI: https://doi.org/10.4213/sm7824

Full text: PDF file (1090 kB)
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English version:
Sbornik: Mathematics, 2012, 203:1, 28–59

Bibliographic databases:

UDC: 517.938.5
MSC: Primary 37J35, 70E05, 70E40; Secondary 37J05
Received: 24.11.2010 and 30.08.2011

Citation: N. S. Logacheva, “Classification of nondegenerate equilibria and degenerate 1-dimensional orbits of the Kovalevskaya-Yehia integrable system”, Mat. Sb., 203:1 (2012), 31–60; Sb. Math., 203:1 (2012), 28–59

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm7824
  • http://mi.mathnet.ru/eng/msb/v203/i1/p31

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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  crossref  mathscinet  zmath  zmath  isi  elib  elib  scopus
    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
  • Математический сборник Sbornik: Mathematics (from 1967)
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