Introduction and examples

Abstract

AbstractThis 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.KeywordsVector FieldInvariant TorusFrequency VectorSmall DivisorDiophantine ConditionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.