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Regular and Chaotic Dynamics, 2000, Volume 5, Issue 4, Pages 437–457
DOI: https://doi.org/10.1070/RD2000v005n04ABEH000158
(Mi rcd889)
 

This article is cited in 16 scientific papers (total in 16 papers)

Fomenko–Zieschang Invariant in the Bogoyavlenskyi Integrable Case

D. B. Zotev

Department of Mathematics, Wolgograd State Pedagogical University, Lenin Avenue, 27, Wolgograd, 400013, Russia
Citations (16)
Abstract: The topology of an integrable Hamiltonian system with two degrees of freedom, occuring in dynamics of the magnetic heavy body with a fixed point [1], is explored. The equations of critical submanifolds of the supplementary integral $f$, restricted to arbitrary isoenergy surface $Q^3_h$, are obtained. In particular, all the phase trajectories of a stable periodic motion are found. It is proved, that $f$ is a Bottean integral. The bifurcation diagram, full Fomenko–Zieschang invariant and the topology of each regular isoenergy surface $Q^3_h$ are calculated, as well as the topology of phase manifold $M^4$, which has a degenerate peculiarity of the symplectic structure. This peculiarity did not appear in dynamics before. A method of the computer visualization of Liouville tori bifurcations is offering.
Received: 20.10.2000
Bibliographic databases:
Document Type: Article
MSC: 22D20, 70E15
Language: English
Citation: D. B. Zotev, “Fomenko–Zieschang Invariant in the Bogoyavlenskyi Integrable Case”, Regul. Chaotic Dyn., 5:4 (2000), 437–457
Citation in format AMSBIB
\Bibitem{Zot00}
\by D. B. Zotev
\paper Fomenko–Zieschang Invariant in the Bogoyavlenskyi Integrable Case
\jour Regul. Chaotic Dyn.
\yr 2000
\vol 5
\issue 4
\pages 437--457
\mathnet{http://mi.mathnet.ru/rcd889}
\crossref{https://doi.org/10.1070/RD2000v005n04ABEH000158}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1810625}
\zmath{https://zbmath.org/?q=an:1005.70007}
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  • This publication is cited in the following 16 articles:
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