This chapter is devoted to center manifold theory. We present a general result on the existence of local center manifolds for infinite-dimensional systems in Section 2.2 and then discuss several particular cases and extensions, as, for instance, to parameter-dependent systems and systems possessing different symmetries in Section 2.3. We give a series of examples showing how these results apply to various situations in Section 2.2.4 and in Section 2.4. A brief description of the tools and results from the theory of linear operators needed in this chapter is given in Appendix A.


Hopf Bifurcation Center Manifold Steady Solution Spectral Projection Algebraic Multiplicity 
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© EDP Sciences 2011

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesUniversité de Franche-ComtéBesançon CedexFrance
  2. 2.Laboratoire J.A.DieudonnéIUF, Université de NiceNice Cedex 02France

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