Regular and Chaotic Dynamics

, Volume 17, Issue 5, pp 451–478 | Cite as

Bifurcation analysis and the Conley index in mechanics

  • Alexey V. Bolsinov
  • Alexey V. Borisov
  • Ivan S. Mamaev
Article

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 

MSC2010 numbers

76M23 34A05 

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • Alexey V. Bolsinov
    • 1
    • 2
  • Alexey V. Borisov
    • 2
  • Ivan S. Mamaev
    • 2
  1. 1.School of MathematicsLoughborough UniversityLoughborough, LeicestershireUK
  2. 2.Institute of Computer ScienceUdmurt State UniversityIzhevskRussia

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