Abstract:
The paper is devoted to the bifurcation analysis and the Conley index in Hamiltonian dynamical systems. We discuss the phenomenon of appearance (disappearance) of equilibrium points under the change of the Morse index of a critical point of a Hamiltonian. As an application of these techniques we find new relative equilibria in the problem of the motion of three point vortices of equal intensity in a circular domain.
This research was supported by the Grant of the Government of the Russian Federation for state support of scientific research conducted under supervision of leading scientists in Russian educational institutions of higher professional education (contract no. 11.G34.31.0039) and the federal target programme “Scientific and Scientific-Pedagogical Personnel of Innovative Russia” (14.740.11.0876). The work was supported by the Grant of the President of the Russian Federation for the Leading Scientific Schools of the Russian Federation (NSh-2519.2012.1).
Citation:
Alexey V. Bolsinov, Alexey V. Borisov, Ivan S. Mamaev, “The Bifurcation Analysis and the Conley Index in Mechanics”, Regul. Chaotic Dyn., 17:5 (2012), 451–478
\Bibitem{BolBorMam12}
\by Alexey V. Bolsinov, Alexey V. Borisov, Ivan S. Mamaev
\paper The Bifurcation Analysis and the Conley Index in Mechanics
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 5
\pages 451--478
\mathnet{http://mi.mathnet.ru/rcd415}
\crossref{https://doi.org/10.1134/S1560354712050073}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2989517}
\zmath{https://zbmath.org/?q=an:1252.76055}
Linking options:
https://www.mathnet.ru/eng/rcd415
https://www.mathnet.ru/eng/rcd/v17/i5/p451
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