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Invariant Manifolds for Semilinear Partial Differential Equations

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Dynamics Reported

Part of the book series: Dynamics Reported ((DYNAMICS,volume 2))

Abstract

When studying the behaviour of a dynamical system in the neighbourhood of an equilibrium point the first step is to construct the stable, unstable and centre manifolds. These are manifolds that are invariant under the flow relative to a neighbourhood of the equilibrium point and carry the solutions that decay or grow (or neither) at certain rates. These ideas have a long history, see for instance Poincaré [32] and Hadamard [11]. Sophisticated recent results can be found in Fenichel [7], Hirsch, Pugh and Shub [17] and Kelley [22].

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Author information

Authors and Affiliations

  1. Department of Mathematics, Brigham Young University, USA

    Peter W. Bates

  2. Department of Mathematics, University of Maryland, USA

    Christopher K. R. T. Jones

Authors
  1. Peter W. Bates
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  2. Christopher K. R. T. Jones
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Editor information

Editors and Affiliations

  1. Mathematics, Swiss Federal Institute of Technology (ETH), CH-8092, Zurich, Switzerland

    Urs Kirchgraber

  2. Mathematics, Ludwig-Maximilians University, D-8000, Munich, Federal Republic of Germany

    Hans Otto Walther

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© 1989 John Wiley & Sons Ltd and B. G. Teubner

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Bates, P.W., Jones, C.K.R.T. (1989). Invariant Manifolds for Semilinear Partial Differential Equations. In: Kirchgraber, U., Walther, H.O. (eds) Dynamics Reported. Dynamics Reported, vol 2. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-96657-5_1

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  • DOI: https://doi.org/10.1007/978-3-322-96657-5_1

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-519-02151-3

  • Online ISBN: 978-3-322-96657-5

  • eBook Packages: Springer Book Archive

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