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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2000, том 5, выпуск 4, страницы 437–457 (Mi rcd889)

Эта публикация цитируется в 16 статьях

Fomenko–Zieschang Invariant in the Bogoyavlenskyi Integrable Case

D. B. Zotev

Department of Mathematics, Wolgograd State Pedagogical University, Lenin Avenue, 27, Wolgograd, 400013, Russia

Аннотация: 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.

MSC: 22D20, 70E15

Поступила в редакцию: 20.10.2000

Язык публикации: английский

DOI: 10.1070/RD2000v005n04ABEH000158



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