الفهرس Only 14 pages are availabe for public view
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Abstract
Mathematics fields are the philosophy of Sciences. There are many branches of mathematics some of them are differential equations, Chaos theory and geometric topology. Chaos theory is the branch of mathematics for the study of processes that seem so complex that at first they do not appear to be governed by any known laws or principles, but which actually have an underlying order that can be described by vector calculus and its associated geometry. The field of differential equations is an important field in many applications. There is an important connection between differential equations, Chaos theory and geometric topology. The present thesis is concerned with the connection between Chaos theory, differential equations and geometric topology. The thesis consist of five chapters: Chapter 1 is just an introductory chapter; it sets the stage for the coming chapters by accommodating some basic concepts and definitions in differential equations and geometry, which are needed in this thesis. In Chapter 2, we discuss the effect of folding and retraCtion of the differential equations on their chaotic solutions and their chaotic differential equations, also we define new types of conditional folding. The limit of the transformations is obtained and some commutative diagrams describing the above transformations are presented. Some applications in chemistry and medicine are presented.