Center manifold theory is essential for analyzing local bifurcations. As the Liapunov-Schmidt reduction for stationary and Hopf bifurcations, center manifold theory is used to reduce a dynamical system near a nonhyperbolic equilibrium or a periodic solution to a low-dimensional system with the vector field as functions of the critical modes. Furthermore, stability of solutions and local dynamics of the system can be derived from the low-dimensional system. The center manifold theorem was introduced in the sixties by Pliss [243] and Kelley [182]. Owing to the Lanford’s contribution [198] this theory has been applied extensively to the study of bifurcation problems and dynamical systems, in particular, in connection with the normal form theory.


Hopf Bifurcation Taylor Expansion Bifurcation Point Critical Mode Center Manifold 
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© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Zhen Mei
    • 1
  1. 1.Department of MathematicsUniversity of MarburgMarburgGermany

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