The Center Manifold Theorem
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 . Most of the essential ideas are also in Kelley  and a treatment with additional references is contained in Hartman . However, we shall follow a proof given by Lanford  which is adapted to the case at hand, and is direct and complete. We thank Professor Lanford for allowing us to reproduce his proof.
KeywordsBanach Space Unit Circle HOPF Bifurcation Spectral Radius Invariant Manifold
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