Overview
- 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
Part of the book series: Nonlinear Systems and Complexity (NSCH, volume 29)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (12 chapters)
-
Front Matter
-
Back Matter
Keywords
About this book
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.
Authors and Affiliations
About the authors
Marat Akhmet
Dr. Marat Akhmet is currently a Professor at Department of Mathematics, Middle East Technical University, Ankara, Turkey. He got his B.S. degree in mathematics at Aktobe State University, Kazakhstan, and Ph.D. degree in differential equations and mathematical physics at Kiev State University, Ukraine. Currently Dr. Marat Akhmet’s researches focus on the dynamical models and differential equations. He has published six books and more than a hundred and fifty scientific papers. In the last several years, he has been investigating dynamics of neural networks, periodic and almost periodic motions, stability, chaos and fractals.
Mehmet Onur FenDr. Mehmet Onur Fen received his B.S. degree in mathematics from Middle East Technical University, Ankara, Turkey, with a double major in physics. He graduated from the mathematics Ph.D. program of the same university in September 2013. Currently he is working as an Associate Professor at Department of Mathematics, TED University, Ankara, Turkey. Dr. Mehmet Onur Fen’s research interests include chaotic dynamical systems, mathematical models of neural networks, and several types of differential equations.
Ejaily Milad Alejaily
Dr. Ejaily Milad Alejaily is currently a lecturer at the College of Engineering Technology, Houn, Libya. He received his B.S. degree in mechanical engineering from Sirte University, Libya in 1997. Later in 2009, Dr. Alejaily obtained his M.S. in mathematics from Universiti Teknologi Malaysia. He graduated from the mathematics Ph.D. program of Middle East Technical University, Ankara, Turkey in August 2019.Bibliographic Information
Book Title: Dynamics with Chaos and Fractals
Authors: Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
Series Title: Nonlinear Systems and Complexity
DOI: https://doi.org/10.1007/978-3-030-35854-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-35853-2Published: 02 January 2020
Softcover ISBN: 978-3-030-35856-3Published: 02 January 2021
eBook ISBN: 978-3-030-35854-9Published: 01 January 2020
Series ISSN: 2195-9994
Series E-ISSN: 2196-0003
Edition Number: 1
Number of Pages: XIII, 226
Number of Illustrations: 5 b/w illustrations, 71 illustrations in colour
Topics: Mathematical Applications in the Physical Sciences, Complexity, Applications of Nonlinear Dynamics and Chaos Theory, Dynamical Systems and Ergodic Theory, Engineering Mathematics