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.
Author(s): Anima Nagar, Manpreet Singh
Series: SpringerBriefs in Mathematics
Publisher: Springer
Year: 2023
Language: English
Pages: 86
City: Singapore
Preface
Contents
About the Authors
1 Introduction
1.1 Introduction
1.2 Chapters' Overview
References
2 Bird's-Eye View on Dynamical Systems
2.1 Definitions and Elementary Properties
2.2 Induced Spaces
2.3 Enveloping Semigroups
2.3.1 Some Basic Theory
2.3.2 Function Spaces
2.4 Symbolic Dynamics
References
3 Dynamics of Induced Systems
3.1 For (semi)Cascades
3.2 For (semi)Flows
References
4 Dynamical Properties of Enveloping Semigroups
4.1 Recurrence in Enveloping Semigroups
4.2 Periodic Points for Enveloping Semigroups
4.3 Finite Minimal Ideals in Enveloping Semigroup and Proximal Relations
4.4 Variations of Transitivity for Enveloping Semigroups
4.4.1 Transitive Enveloping Semigroups
4.4.2 Stronger Forms of Transitivity for Enveloping Semigroups
References
5 Enveloping Semigroup of the Induced Systems
5.1 Inducible Mappings
5.2 Enveloping Semigroup of (2Z, σ), Its Subshifts and of (22Z,σ*)
5.2.1 Isomorphism of βZ and βnZ, foralln inN
5.3 Saturated Enveloping Semigroups
References
