The Center Manifold Theorem

  • J. E. Marsden
  • M. McCracken
Part of the Applied Mathematical Sciences book series (AMS, volume 19)


In this section we will start to carry out the program outlined in Section 1 by proving the center manifold theorem. The general invariant manifold theorem is given in Hirsch-Pugh-Shub [1]. Most of the essential ideas are also in Kelley [1] and a treatment with additional references is contained in Hartman [1]. However, we shall follow a proof given by Lanford [1] which is adapted to the case at hand, and is direct and complete. We thank Professor Lanford for allowing us to reproduce his proof.


Banach Space Unit Circle HOPF Bifurcation Spectral Radius Invariant Manifold 
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Copyright information

© Springer-Verlag New York Inc. 1976

Authors and Affiliations

  • J. E. Marsden
    • 1
  • M. McCracken
    • 2
  1. 1.Department of MathematicsUniversity of California at BerkeleyUSA
  2. 2.Department of MathematicsUniversity of California at Santa CruzUSA

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