In this introductory chapter we want to give a brief survey of results on invariant manifolds and fibers in infinite dimensions as well as describe the aims and scope of this monograph. Recent books by Wiggins  and Bronstein and Kopanskii  survey invariant manifold results in finite dimensions. Here we will be focusing solely on surveying results in the infinite-dimensional setting.
KeywordsInvariant Manifold Unstable Manifold Stable Manifold Center Manifold Invariant Torus
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