Dynamics with Chaos and Fractals / Nonlinear Systems and Complexity Bd.29 (PDF)
(Sprache: Englisch)
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...
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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
Autoren-Porträt von Marat Akhmet, Mehmet Onur Fen, Ejaily Milad Alejaily
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 Fen
Dr. 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.
Bibliographische Angaben
- Autoren: Marat Akhmet , Mehmet Onur Fen , Ejaily Milad Alejaily
- 2020, 1st ed. 2020, 226 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3030358542
- ISBN-13: 9783030358549
- Erscheinungsdatum: 01.01.2020
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
eBook Informationen
- Dateiformat: PDF
- Größe: 8.03 MB
- Ohne Kopierschutz
- Vorlesefunktion
Sprache:
Englisch
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