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Spatio-Temporal Dynamics of Reaction-Diffusion Patterns

  • Bernold Fiedler
  • Arnd Scheel

Abstract

In this survey we look at parabolic partial differential equations from a dynamical systems point of view. With origins deeply rooted in celestial mechanics, and many modern aspects traceable to the monumental influence of Poincaré, dynamical systems theory is mainly concerned with the global time evolution T(t)u 0 of points u 0 — and of sets of such points — in a more or less abstract phase space X. The success of dynamical concepts such as gradient flows, invariant manifolds, ergodicity, shift dynamics, etc. during the past century has been enormous — both as measured by achievement, and by vitality in terms of newly emerging questions and long-standing open problems.

Keywords

Hopf Bifurcation Global Attractor Essential Spectrum Spiral Wave Morse Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Bernold Fiedler
    • 1
  • Arnd Scheel
    • 2
  1. 1.FB Mathematik IFreie Universität BerlinBerlinGermany
  2. 2.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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