This volume consists of six articles covering different facets of the mathematical theory of dynamical systems. The topics range from topological foundations through invariant manifolds, decoupling, perturbations and computations to control theory. All contributions are based on a sound mathematical analysis. Some of them provide detailed proofs while others are of a survey character. In any case, emphasis is put on motivation and guiding ideas. Many examples are included.The papers of this volume grew out of a tutorial workshop for graduate students in mathematics held at the University of Augsburg. Each of the contributions is self-contained and provides an in-depth insight into some topic of current interest in the mathematical theory of dynamical systems. The text is suitable for courses and seminars on a graduate student level.
Dynamical systems - the topological foundations, E. Akin; integral manifolds for Caratheodory type differential equations in Banach spaces, B. Aulbach and T. Wanner; control theory and dynamical systems, F. Colonius and W. Kliemann; perturbation of invariant manifolds of ordinary differential equations, G. Osipenko; shadowing in discrete dynamical systems, B.A. Coomes et al; reduction of discrete dynamical and semidynamical systems in metric spaces, A. Reinfelds.