Topological Dynamics of Enveloping Semigroups

This book introduces the theory of enveloping semigroups—an important tool in the field of topological dynamics—introduced by Robert Ellis. The book deals with the basic theory of topological dynamics and touches on the advanced concepts of the dynamics of induced systems and their enveloping semigroups. All the chapters in the book are well organized and systematically dealing with introductory topics through advanced research topics. The basic concepts give the motivation to begin with, then the theory, and finally the new research-oriented topics. The results are presented with detailed proof, plenty of examples and several open questions are put forward to motivate for future research. Some of the results, related to the enveloping semigroup, are new to the existing literature. The enveloping semigroups of the induced systems is considered for the first time in the literature, and some new results are obtained. The book has a research-oriented flavour in the field of topological dynamics.

Introduction.- Basic Definitions and Elementary Properties.- Dynamics of Induced Systems.- Dynamical Properties of Enveloping Semigroups.- Enveloping Semigroup of the Induced Systems.- More Investigations.

ANIMA NAGAR is Associate Professor at the Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India. She completed her doctoral studies at Gujarat University in 1999 and spent her postdoctoral years at the University of Hyderabad, India. She has mainly held visiting positions at the University of Maryland, USA, and Technical University Wein as well as the University of Wein, Austria. Her research interests are in topological dynamics and symbolic dynamics.

MANPREET SINGH is a visiting scientist at the Indian Statistical Institute, Bengaluru, India. The author completed his Ph.D. degree from the Indian Institute of Technology Delhi. His broad research area is topological dynamics. He is mainly interested in the relation between enveloping semigroup of a flow and the enveloping semigroup of its induced flow.