Invariant Manifolds for Semilinear Partial Differential Equations

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 Poincare [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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