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.
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