This book is designed as an introduction into what I call 'abstract' Topological Dynamics (TO): the study of topological transformation groups with respect to problems that can be traced back to the qualitative theory of differential equa is in the tradition of the books GH] and EW. The title tions. So this book (, Elements . . . ' rather than 'Introduction . . . ') does not mean that this book should be compared, either in scope or in (intended) impact, with the 'Ele ments' of Euclid or Bourbaki. Instead, it reflects the choice and organisation of the material in this book: elementary and...

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...

There is no recent elementary introduction to the theory of discrete dynamical systems that stresses the topological background of the topic. This book fills this gap: it deals with this theory as 'applied general topology'. We treat all important concepts needed to understand recent literature. The book is addressed primarily to graduate students. The prerequisites for understanding this book are modest: a certain mathematical maturity and course in General Topology are sufficient.