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Regul. Chaotic Dyn., 2012, Volume 17, Issue 5, Pages 451–478 (Mi rcd415)  

This article is cited in 8 scientific papers (total in 8 papers)

The Bifurcation Analysis and the Conley Index in Mechanics

Alexey V. Bolsinovab, Alexey V. Borisovb, Ivan S. Mamaevb

a School of Mathematics, Loughborough University, United Kingdom, LE11 3TU, Loughborough, Leicestershire
b Institute of Computer Science, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia

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.

Keywords: Morse index, Conley index, bifurcation analysis, bifurcation diagram, Hamiltonian dynamics, fixed point, relative equilibrium

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 11.G34.31.0039
14.740.11.0876
NSh-2519.2012.1
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).


DOI: https://doi.org/10.1134/S1560354712050073


Bibliographic databases:

Document Type: Article
MSC: 76M23, 34A05
Received: 21.09.2011
Language: English

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

Citation in format AMSBIB
\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://www.ams.org/mathscinet-getitem?mr=2989517}
\zmath{https://zbmath.org/?q=an:1252.76055}


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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. Sergei V. Sokolov, Sergei M. Ramodanov, “Falling Motion of a Circular Cylinder Interacting Dynamically with a Point Vortex”, Regul. Chaotic Dyn., 18:1-2 (2013), 184–193  mathnet  crossref  mathscinet  zmath
    2. Alexey V. Borisov, Ivan S. Mamaev, “Topological Analysis of an Integrable System Related to the Rolling of a Ball on a Sphere”, Regul. Chaotic Dyn., 18:4 (2013), 356–371  mathnet  crossref  mathscinet  zmath
    3. 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
    4. P. E. Ryabov, A. Yu. Savushkin, “Fazovaya topologiya volchka Kovalevskoi – Sokolova”, Nelineinaya dinam., 11:2 (2015), 287–317  mathnet
    5. A. V. Borisov, P. E. Ryabov, S. V. Sokolov, “Bifurcation Analysis of the Motion of a Cylinder and a Point Vortex in an Ideal Fluid”, Math. Notes, 99:6 (2016), 834–839  mathnet  crossref  crossref  mathscinet  isi  elib
    6. 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
    7. Leonid G. Kurakin, Irina V. Ostrovskaya, Mikhail A. Sokolovskiy, “On the Stability of Discrete Tripole, Quadrupole, Thomson’ Vortex Triangle and Square in a Two-layer/Homogeneous Rotating Fluid”, Regul. Chaotic Dyn., 21:3 (2016), 291–334  mathnet  crossref  mathscinet
    8. Leonid G. Kurakin, Irina V. Ostrovskaya, “On Stability of Thomson’s Vortex $N$-gon in the Geostrophic Model of the Point Bessel Vortices”, Regul. Chaotic Dyn., 22:7 (2017), 865–879  mathnet  crossref
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