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Hello I have started working on my PhD a short while ago and wondered if there might be any good introductions to spatial dynamics.

I have a basic understanding of dynamical systems but would like to expand further on it.

Thank you for your recommendations.

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    $\begingroup$ This is a bit broad. What is your advisor suggesting? $\endgroup$
    – András Bátkai
    Commented Jan 18, 2016 at 13:24
  • $\begingroup$ For the beginning he suggested the notes dam.brown.edu/people/sandsted/documents/… to me. I'm sorry I should have been more specific about my intentions: I would like to understand the center manifold theorem a bit better and the reduction of pdes to systems of odes in an infinite dimensional space. $\endgroup$
    – lKyouma
    Commented Jan 18, 2016 at 13:42
  • $\begingroup$ Dan Henry's Geometric Theory of Semilinear Parabolic Equations is a classic. $\endgroup$
    – Aaron Hoffman
    Commented Jan 19, 2016 at 21:20

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Based on your comment, the book

M. Haragus, G. Iooss: Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems, Springer, 2011

might be of some interest to you.

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Robinson: Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors

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