Description

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This book considers for the first time chaos for a single motion that implies chaotic behavior of infinite neighbors and makes the property generic for the dynamics. It also considers fractals as geometrical objects--very popular nowadays for their complexity, sophisticated structure, and ubiquity in the natural world and in modern engineering. Recent research presented herein suggests ways for how to map fractals, and explains how the mapping can easily be applied to realize discrete and continuous dynamics in fractals and for fractals. The authors also introduce the use of special functional space and new, unpredictable functions determined on the real axis, continuous and bounded. Thus, they describe an extension of oscillations theory for differential and discrete equations for unpredictable, sensitive, and irregular phenomena. Novel results for the unpredictable solutions are further obtained and basic properties and methods of verification are developed.
The book is written by mathematicians and it contains results that are rigorously proven. The material explained in this volume is highly relevant for those working in applied mathematics with a strong theoretical approach. It is indisputable that chaos and fractals are very connected, which is why it is natural that these two subjects are united in this single book.

About the Author

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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.