Introduction and examples

Abstract

This book investigates the occurrence of quasi-periodic motions in dynamical systems with special emphasis on the persistence of these motions under small perturbations of the system. Quasi-periodic motions densely fill up invariant tori, therefore this study can be regarded as a part of a more general theory of invariant manifolds. The existence, persistence and other properties of invariant manifolds play a fundamental rôle in the analysis of nonlinear dynamical systems [67,115,158,356]. In this book we confine ourselves with finite dimensional systems. For the theory of quasi-periodic motions in infinite dimensional dynamical systems, the reader is recommended to consult, e.g., [185,186,279–281] and references therein.