Nagar A., Singh M. Topological Dynamics of Enveloping Semigroups

Singapore: Springer, 2023. — 87 p.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.Preface
About the Authors
Introduction
Introduction
Chapters' Overview
References
Bird's-Eye View on Dynamical Systems
Definitions and Elementary Properties
Induced Spaces
Enveloping Semigroups
Some Basic Theory
Function Spaces
Symbolic Dynamics
References
Dynamics of Induced Systems
For (semi)Cascades
For (semi)Flows
References
Dynamical Properties of Enveloping Semigroups
Recurrence in Enveloping Semigroups
Periodic Points for Enveloping Semigroups
Finite Minimal Ideals in Enveloping Semigroup and Proximal Relations
Variations of Transitivity for Enveloping Semigroups
Transitive Enveloping Semigroups
Stronger Forms of Transitivity for Enveloping Semigroups
References
Enveloping Semigroup of the Induced Systems
Inducible Mappings
Enveloping Semigroup of (2Z, σ), Its Subshifts and of (22Z,σ*)
Isomorphism of βZ and βnZ, foralln inN
Saturated Enveloping Semigroups
References