Elements of Topological Dynamics

ISBN-13: 9789048142743 / Angielski / Miękka / 2010 / 748 str.

J. De Vries

Opis

This major volume presents a comprehensive introduction to the study of topological transformation groups with respect to topological problems which can be traced back to the qualitative theory of differential equations, and provides a systematic exposition of the fundamental methods and techniques of abstract topological dynamics. The contents can be divided into two parts. The first part is devoted to a broad overview of the topological aspects of the theory of dynamical systems (including shift systems and geodesic and horocycle flows). Part Two is more specialized and presents in a systematic way the fundamental techniques and methods for the study of compact minima flows and their morphisms. It brings together many results which are scattered throughout the literature, and, in addition, many examples are worked out in detail. The primary purpose of this book is to bridge the gap between the beginner' and the specialist in the field of topological dynamics. All proofs are therefore given in detail. The book will, however, also be useful to the specialist and each chapter concludes with additional results (without proofs) and references to sources and related material. The prerequisites for studying the book are a background in general toplogy and (classical and functional) analysis. For graduates and researchers wishing to have a good, comprehensive introduction to topological dynamics, it will also be of great interest to specialists. This volume is recommended as a supplementary text.

Spis treści

Preface. Notation. I: Various aspects of the theory of dynamical systems. II: Continuous and discrete flows. III: Important examples. IV: The general framework. V: Equicontinuity and distality. VI: Structure of extensions. Appendices: A: Topology. B: Compact right semitopological semigroups. C: Integration. D: Enveloping semigroups and compactifications. E: Topological transformation groups. References. Index of authors. Index of symbols. Index of terms.