Bifurcation analysis and the Conley index in mechanics

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• 作者：Alexey V. Bolsinov (12) A.Bolsinov@lboro.ac.uk
  Alexey V. Borisov (2) borisov@rcd.ru
  Ivan S. Mamaev (2) mamaev@rcd.ru
• 关键词：Morse index – ; Conley index – ; bifurcation analysis – ; bifurcation diagram – ; Hamiltonian dynamics – ; fixed point – ; relative equilibrium
• 刊名：Regular and Chaotic Dynamics
• 出版年：2012
• 出版时间：September 2012
• 年：2012
• 卷：17
• 期：5
• 页码：451-478
• 全文大小：1.5 MB
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• 作者单位：1. School of Mathematics, Loughborough University, UK LE11 3TU Loughborough, Leicestershire2. Institute of Computer Science, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
• ISSN：1468-4845

文摘

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.