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Regul. Chaotic Dyn., 2005, Volume 10, Issue 4, Pages 381–398 (Mi rcd716)  

This article is cited in 10 scientific papers (total in 10 papers)

Bicentennial of C.G. Jacobi

Bifurcation diagrams of the Kowalevski top in two constant fields

M. P. Kharlamov

Volgograd Academy for Public Administration, 8, Gagarina St., Volgograd 400131, Russia

Abstract: The Kowalevski top in two constant fields is known as the unique profound example of an integrable Hamiltonian system with three degrees of freedom not reducible to a family of systems in fewer dimensions. As the first approach to topological analysis of this system we find the critical set of the integral map; this set consists of the trajectories with number of frequencies less than three. We obtain the equations of the bifurcation diagram in $\bold{R}^3$. A correspondence to the Appelrot classes in the classical Kowalevski problem is established. The admissible regions for the values of the first integrals are found in the form of some inequalities of general character and boundary conditions for the induced diagrams on energy levels.

Keywords: Kowalevski top, double field, critical set, bifurcation diagrams

DOI: https://doi.org/10.1070/RD2005v010n04ABEH000321


Bibliographic databases:

MSC: 70E17, 70G40
Received: 09.04.2005
Accepted:11.06.2005
Language:

Citation: M. P. Kharlamov, “Bifurcation diagrams of the Kowalevski top in two constant fields”, Regul. Chaotic Dyn., 10:4 (2005), 381–398

Citation in format AMSBIB
\Bibitem{Kha05}
\by M. P. Kharlamov
\paper Bifurcation diagrams of the Kowalevski top in two constant fields
\jour Regul. Chaotic Dyn.
\yr 2005
\vol 10
\issue 4
\pages 381--398
\mathnet{http://mi.mathnet.ru/rcd716}
\crossref{https://doi.org/10.1070/RD2005v010n04ABEH000321}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2191368}
\zmath{https://zbmath.org/?q=an:1133.70306}


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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. B. Zot'ev, “Contact degeneracies of closed 2-forms”, Sb. Math., 198:4 (2007), 491–520  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. M. P. Kharlamov, “Topologicheskii analiz i bulevy funktsii: I. Metody i prilozheniya k klassicheskim sistemam”, Nelineinaya dinam., 6:4 (2010), 769–805  mathnet
    3. I. I. Kharlamova, P. E. Ryabov, “Elektronnyi atlas bifurkatsionnykh diagramm girostata Kovalevskoi–Yakhya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 2, 147–162  mathnet  elib
    4. M. P. Kharlamov, P. E. Ryabov, “Diagrammy Smeila–Fomenko i grubye invarianty sluchaya Kovalevskoi–Yakhya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 4, 40–59  mathnet
    5. P. E. Ryabov, M. P. Kharlamov, “Classification of singularities in the problem of motion of the Kovalevskaya top in a double force field”, Sb. Math., 203:2 (2012), 257–287  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. P. E. Ryabov, “Phase topology of one irreducible integrable problem in the dynamics of a rigid body”, Theoret. and Math. Phys., 176:2 (2013), 1000–1015  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. Mikhail P. Kharlamov, “Extensions of the Appelrot Classes for the Generalized Gyrostat in a Double Force Field”, Regul. Chaotic Dyn., 19:2 (2014), 226–244  mathnet  crossref  mathscinet  zmath
    8. P. E. Ryabov, A. Yu. Savushkin, “Fazovaya topologiya volchka Kovalevskoi – Sokolova”, Nelineinaya dinam., 11:2 (2015), 287–317  mathnet
    9. 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
    10. Vladimir Dragovich, Katarina Kukić, “Discriminantly separable polynomials and the generalized Kowalevski top”, Theor. Appl. Mech., 44:2 (2017), 229–236  mathnet  crossref
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