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Эта публикация цитируется в 16 научных статьях (всего 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.
Поступила в редакцию: 20.10.2000
Образец цитирования:
D. B. Zotev, “Fomenko–Zieschang Invariant in the Bogoyavlenskyi Integrable Case”, Regul. Chaotic Dyn., 5:4 (2000), 437–457
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd889 https://www.mathnet.ru/rus/rcd/v5/i4/p437
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