Abstract
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.
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© 1976 Springer-Verlag New York Inc.
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Marsden, J.E., McCracken, M. (1976). The Center Manifold Theorem. In: The Hopf Bifurcation and Its Applications. Applied Mathematical Sciences, vol 19. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6374-6_2
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DOI: https://doi.org/10.1007/978-1-4612-6374-6_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90200-5
Online ISBN: 978-1-4612-6374-6
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