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Topological Dynamics of Enveloping Semigroups

  • Book
  • © 2022

Overview

Authors:
  1. Anima Nagar

    1. Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India

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  2. Manpreet Singh

    1. Indian Institute of Science, Bengaluru, India

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  • Discusses the theory of enveloping semigroups
  • Deals with the basic theory of topological dynamics
  • introduces the advanced concepts of the dynamics of induced systems and their enveloping semigroups

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Introduction

    • Anima Nagar, Manpreet Singh
    Pages 1-5

  3. Bird’s-Eye View on Dynamical Systems

    • Anima Nagar, Manpreet Singh
    Pages 7-31

  4. Dynamics of Induced Systems

    • Anima Nagar, Manpreet Singh
    Pages 33-44

  5. Dynamical Properties of Enveloping Semigroups

    • Anima Nagar, Manpreet Singh
    Pages 45-61

  6. Enveloping Semigroup of the Induced Systems

    • Anima Nagar, Manpreet Singh
    Pages 63-81
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India

    Anima Nagar

  • Indian Institute of Science, Bengaluru, India

    Manpreet Singh

About the authors

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.

Bibliographic Information

  • Book Title: Topological Dynamics of Enveloping Semigroups

  • Authors: Anima Nagar, Manpreet Singh

  • Series Title: SpringerBriefs in Mathematics

  • DOI: https://doi.org/10.1007/978-981-19-7877-7

  • Publisher: Springer Singapore

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022

  • Softcover ISBN: 978-981-19-7876-0Published: 02 January 2023

  • eBook ISBN: 978-981-19-7877-7Published: 01 January 2023

  • Series ISSN: 2191-8198

  • Series E-ISSN: 2191-8201

  • Edition Number: 1

  • Number of Pages: IX, 81

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Topology, Topological Groups, Lie Groups

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