Concepts From Dynamical Systems

Abstract

This chapter is a survey of facts and results from dynamical systems theory that are used throughout the book. Our primary goal is to fix notation and terminology for later chapters, and recall some aspects of the theory that are usually not discussed in introductory books. For the sake of easier reading, we keep the discussion informal, avoiding technical notation and proofs as much as possible. While most omitted details can be found in graduate level introductory books to dynamical systems, some of the more advanced topics are covered only in research articles. In either case, we shall supply references that treat the subject in greater depth. In addition, we encourage the reader to use Appendices A and B as references on the basics of differential geometry and functional analysis.