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Introduction to Topological Dynamical Systems I
Mohammed Nokhas Murad Kaki
Published Date:
July, 2016
Science Publishing Group
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Table of Contents
The Whole Book
Front Matter
Chapter 1 New Types of Topological Transitivity
1.1 Introduction
1.2 Preliminaries and Definitions
1.3 λ-Type Transitive Maps and Topological λr-Conjugacy
1.4 New Types of Chaos of Topological Spaces
1.5 Chaos in Product Topological Spaces
1.6 Conclusion
Chapter 2 Topologically α-Type Maps and Wandering Points
2.1 Introduction
2.2 Preliminaries and Definitions
2.3 α-Type Transitivity and α-Minimal Maps
2.4 α-Minimal Maps: And α-Minimal Sets
2.5 Separable Topological Spaces
2.6 Topological α-Type Transitive on Product Spaces
2.7. Alpha-Type Chaos in Products
2.8 Conclusion
Chapter 3 New Types of Topological b-Transitive Functions
3.1 Introduction
3.2 Preliminaries and Definitions
3.3 b-Transitive and b-Minimal Systems
3.4 Topologically b-Transitive Functions
3.5 Topologically b-Minimal Systems
3.6 Exact, Weakly b-Mixing and Chaos
Chapter 4 Topological δ-Type Transitive Function
4.1 Introduction
4.2 Preliminaries and Definitions
4.3 δ-Type Transitive Functions and δ-Minimal Systems
4.4 Conclusion
Chapter 5 Introduction to Weakly b-Transitive Maps
5.1 Introduction
5.2 Transitivity and Minimal Systems
5.3 Conclusion
Chapter 6 Topologically γ Transitiviy
6.1 Introduction
6.2 Preliminaries and Definitions
6.3 Transitive and Minimal Systems
6.4 Minimal Functions
6.5 Topological Systems and Conjugacy
6.6 Conclusion
Chapter 7 Topologically θ-Type Transitive Maps
7.1 Introduction
7.2 Basic Definitions and Theorems
7.3 Transitive on Product Spaces
7.4 θ-Type Transitive Maps
7.5 Topological θ-Minimal Maps
7.6 Conclusion
Back Matter
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.
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.
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