Center Manifolds

Abstract

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.