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Mat. Sb., 2012, Volume 203, Number 4, Pages 3–46 (Mi msb7868)  

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

Bifurcation sets in the Kovalevskaya-Yehia problem

P. P. Andreyanov, K. E. Dushin

M. V. Lomonosov Moscow State University

Abstract: The two-parameter family of bifurcation diagrams $\Sigma$ of the moment map is investigated in the integrable Kovalevskaya-Yehia case for the motion of a rigid body. A method is developed which is useful for calculating the bifurcation set $\Theta$ in the parameter space which corresponds to bifurcations of diagrams in $\Sigma$ and for classifying these bifurcations. The properties of the sets $\Sigma$ and $\Theta$ are thoroughly investigated, and details of the modifications the bifurcation diagrams undergo as the value of the parameter crosses $\Theta$ are described. Illustrations which explain the structure of the different types of diagram and their interrelations are given.
Bibliography: 22 titles.

Keywords: Kovalevskaya-Yehia problem, integrable systems, bifurcation diagrams.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm7868

Full text: PDF file (966 kB)
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English version:
Sbornik: Mathematics, 2012, 203:4, 459–499

Bibliographic databases:

UDC: 517.538
MSC: 37J20, 37J35, 70E05, 70E40
Received: 25.03.2011

Citation: P. P. Andreyanov, K. E. Dushin, “Bifurcation sets in the Kovalevskaya-Yehia problem”, Mat. Sb., 203:4 (2012), 3–46; Sb. Math., 203:4 (2012), 459–499

Citation in format AMSBIB
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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. 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
    2. El-Sabaa F.M., Hosny M., Zakria S.K., “Bifurcations of Liouville Tori of a Two Fixed Center Problem”, Astrophys. Space Sci., 363:4 (2018), 77  crossref  mathscinet  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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