Dynamics with Chaos and Fractals
暫譯: 混沌與分形的動力學

Akhmet, Marat, Fen, Mehmet Onur, Alejaily, Ejaily Milad

Dynamics with Chaos and Fractals

相關主題

商品描述

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.


商品描述(中文翻譯)

本書探討混沌與分形的概念，這些概念在過去幾十年中屬於動態系統、幾何學、測度理論、拓撲學和數值分析的範疇。書中揭示了一種特殊的泊松穩定點，我們稱之為不可預測點，這種點導致了準最小集合中混沌的存在。這是文獻中首次從單一運動出發描述混沌。混沌現在被置於振盪的範疇，因此，它成為動態系統理論和微分方程框架下的研究主題，如本書所述。書中介紹的技術使得發展連續和離散動力學成為可能，這些動力學允許分形作為軌跡的點以及軌道本身。為了提供強有力的論據支持混沌在現實和抽象宇宙中的普遍性，提出了抽象相似性的概念。

作者簡介

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.


作者簡介(中文翻譯)

**Marat Akhmet**
馬拉特·阿赫梅特博士目前是土耳其安卡拉中東科技大學數學系的教授。他在哈薩克斯坦的阿克托貝國立大學獲得數學學士學位，並在烏克蘭基輔國立大學獲得微分方程和數學物理的博士學位。目前，馬拉特·阿赫梅特博士的研究重點是動態模型和微分方程。他已出版六本書籍和超過一百五十篇科學論文。在過去幾年中，他一直在研究神經網絡的動力學、周期性和幾乎周期性運動、穩定性、混沌和分形。

**Mehmet Onur Fen**
梅赫梅特·奧努爾·芬博士在土耳其安卡拉的中東科技大學獲得數學學士學位，並輔修物理學。他於2013年9月從同一大學的數學博士課程畢業。目前，他在土耳其安卡拉的TED大學數學系擔任副教授。梅赫梅特·奧努爾·芬博士的研究興趣包括混沌動力系統、神經網絡的數學模型以及幾種類型的微分方程。

**Ejaily Milad Alejaily**
艾賈伊·米拉德·阿萊賈伊博士目前是利比亞霍恩工程技術學院的講師。他於1997年在利比亞的西爾特大學獲得機械工程學士學位。隨後在2009年，阿萊賈伊博士在馬來西亞科技大學獲得數學碩士學位。他於2019年8月從土耳其安卡拉的中東科技大學數學博士課程畢業。

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