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Dynamics with Chaos and Fractals

  • Marat Akhmet
  • Mehmet Onur Fen
  • Ejaily Milad Alejaily
Book

Part of the Nonlinear Systems and Complexity book series (NSCH, volume 29)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
    Pages 1-14
  3. Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
    Pages 15-23
  4. Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
    Pages 25-40
  5. Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
    Pages 41-56
  6. Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
    Pages 57-79
  7. Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
    Pages 81-95
  8. Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
    Pages 97-108
  9. Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
    Pages 109-124
  10. Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
    Pages 125-137
  11. Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
    Pages 139-172
  12. Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
    Pages 173-202
  13. Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
    Pages 203-221
  14. Back Matter
    Pages 223-226

About this book

Introduction

The book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. This is the first time in the literature that the description of chaos is initiated from a single motion. Chaos is now placed on the line of oscillations, and therefore, it is a subject of study in the framework of the theories of dynamical systems and differential equations, as in this book. The techniques introduced in the book make it possible to develop continuous and discrete dynamics which admit fractals as points of trajectories as well as orbits themselves. To provide strong arguments for the genericity of chaos in the real and abstract universe, the concept of abstract similarity is suggested.

The Book

  • Stands as the first book presenting theoretical background on the unpredictable point and mapping of fractals
  • Introduces the concepts of unpredictable functions, abstract self-similarity, and similarity map
  • Discusses unpredictable solutions of quasilinear ordinary and functional differential equations
  • Illustrates new ways to construct fractals based on the ideas of Fatou and Julia
  • Examines unpredictability in ocean dynamics and neural networks, chaos in hybrid systems on a time scale, and homoclinic and heteroclinic motions in economic models

 

Keywords

Chaos and fractals differential equations difference equations chaos generation chaos control extension of chaos chaos synchronization

Authors and affiliations

  • Marat Akhmet
    • 1
  • Mehmet Onur Fen
    • 2
  • Ejaily Milad Alejaily
    • 3
  1. 1.Department of MathematicsMiddle East Technical UniversityÇankayaTurkey
  2. 2.Department of MathematicsTED UniversityÇankayaTurkey
  3. 3.Department of Fundamental SciencesCollege of Engineering TechnologyHounLibya

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-35854-9
  • Copyright Information Springer Nature Switzerland AG 2020
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-35853-2
  • Online ISBN 978-3-030-35854-9
  • Series Print ISSN 2195-9994
  • Series Online ISSN 2196-0003
  • Buy this book on publisher's site