Introduction to Topological Dynamical Systems I

Mohammed Nokhas Murad Kaki  © by the authors

ISBN: 978-1-940366-52-4
Published Date: July, 2016
Pages: 166
Paperback: $90
E-book: $25
Publisher: Science Publishing Group
Publication Status: Published
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Book Description

This book is intended as a survey article on new types of transitivity and chaoticity of a topological dynamical system given by a continuous self-map of a locally compact Hausdorff space. On one hand it introduces postgraduate students to the study new types of topological transitivity and gives an overview of new results on the topic, but, on the other hand, it covers some of the recent developments of mathematical science, chaos theory, technology, electronic and computer science. In this project, the author starts with some basic introductory definitions of chaos, which in particular are due to work by Devaney, before he explains the main new ingredients of alpha-type chaos, alpha-type transitivity, alpha-denseness of periodic points in a space with alpha-topology. Then he illustrates by examples and theorems the relevant topologically transitive and chaotic behavior by some maps defined on locally compact Hausdorff spaces and relationship between the new and basic definitions are given.

Author Introduction

Dr. Mohammed Nokhas Murad Kaki, the lead author of this book, is assistant professor of Mathematics department, Faculty of science and science Education, University of Sulaimani, Iraq. He holds a MSc., Ph.D. degree in mathematics and Sc.D. degree in Science. He is interested in sustainable development of mathematical science.

Table of Contents
  • The Whole Book

  • Front Matter

  • Chapter 1 New Types of Topological Transitivity

    1. 1.1 Introduction
    2. 1.2 Preliminaries and Definitions
    3. 1.3 λ-Type Transitive Maps and Topological λr-Conjugacy
    4. 1.4 New Types of Chaos of Topological Spaces
    5. 1.5 Chaos in Product Topological Spaces
    6. 1.6 Conclusion
  • Chapter 2 Topologically α-Type Maps and Wandering Points

    1. 2.1 Introduction
    2. 2.2 Preliminaries and Definitions
    3. 2.3 α-Type Transitivity and α-Minimal Maps
    4. 2.4 α-Minimal Maps: And α-Minimal Sets
    5. 2.5 Separable Topological Spaces
    6. 2.6 Topological α-Type Transitive on Product Spaces
    7. 2.7. Alpha-Type Chaos in Products
    8. 2.8 Conclusion
  • Chapter 3 New Types of Topological b-Transitive Functions

    1. 3.1 Introduction
    2. 3.2 Preliminaries and Definitions
    3. 3.3 b-Transitive and b-Minimal Systems
    4. 3.4 Topologically b-Transitive Functions
    5. 3.5 Topologically b-Minimal Systems
    6. 3.6 Exact, Weakly b-Mixing and Chaos
  • Chapter 4 Topological δ-Type Transitive Function

    1. 4.1 Introduction
    2. 4.2 Preliminaries and Definitions
    3. 4.3 δ-Type Transitive Functions and δ-Minimal Systems
    4. 4.4 Conclusion
  • Chapter 5 Introduction to Weakly b-Transitive Maps

    1. 5.1 Introduction
    2. 5.2 Transitivity and Minimal Systems
    3. 5.3 Conclusion
  • Chapter 6 Topologically γ Transitiviy

    1. 6.1 Introduction
    2. 6.2 Preliminaries and Definitions
    3. 6.3 Transitive and Minimal Systems
    4. 6.4 Minimal Functions
    5. 6.5 Topological Systems and Conjugacy
    6. 6.6 Conclusion
  • Chapter 7 Topologically θ-Type Transitive Maps

    1. 7.1 Introduction
    2. 7.2 Basic Definitions and Theorems
    3. 7.3 Transitive on Product Spaces
    4. 7.4 θ-Type Transitive Maps
    5. 7.5 Topological θ-Minimal Maps
    6. 7.6 Conclusion
  • Back Matter