
Author(s)  Vries, J. de 

Title  Elements of Topological Dynamics 
Publisher  Kluwer Academic Publishers 
Year of publication  1993 
Reviewed by  Mihai Postolache 
Dynamical systems can be found at various places in life and social sciences, notably in applied and theoretical physics, chemistry, computer science etc. In addition, they appear in discrete mathematics.
Elements of Topological Dynamics is a graduate level book for scientists or researchers. It is also suitable for an advanced course on dynamical systems covering both elementary notions about the theory of dynamical systems, continuous and discrete flows together important examples as well as more specialized notions such that compact minima flows and their applications. The material is organized so as to introduce as soon as possible these concepts. Containing a deeply but coherent treatment of various concepts, the book can be used with advantage by prospective mathematicians from universities and, perhaps, by mathematically inclined engineers.
This important volume includes six comprehensive chapters, five appendices which deal with topics such that: topology, compact right semitopological semigroups, integration, enveloping semigroups and compactifications, topological transformation groups as well as preface, index of authors and index of symbols, table of contents aufficiently detailed and a comprehensive bibliography. Each chapter is finished with interesting historical notes and comments.
Intended to attract readers interested both in theory and applications the book furnishes many worked examples for almost every section. The examples allow the reader to understand some results. Many pictures, carefully plotted, illustrate the ideas and the concepts. This research level book is very well written all concepts being clearly presented. The big majority of stated results include complete proofs but there are cases when the reader is counselled to use the bibliography.
In my opinion, this major material provides a good introduction to the stated subject. The book being very high specialized is designed mainly for the institutional market and for individuals seriously interested in the topic. Reading calls for acquaintance with the elements of general topology as well as classical analysis.