
Chaos in Discrete Dynamical Systems: A Visual Introduction in 2 Dimensions By Ralph H. AbrahamEnglish  PDF  1997  257 Pages  ISBN : 1461273471  21.92 MB Chaos Theory is a synonym for dynamical systems theory, a branch of mathematics. Dynamical systems come in three flavors: flows (continuous dynamical systems), cascades (discrete, reversible, dynamical systems), and semicascades (discrete, irreversible, dynamical systems). Chaos Theory is a synonym for dynamical systems theory, a branch of mathematics. Dynamical systems come in three flavors: flows (continuous dynamical systems), cascades (discrete, reversible, dynamical systems), and semicascades (discrete, irreversible, dynamical systems). Flows and semicascades are the classical systems iuntroduced by Poincare a centry ago, and are the subject of the extensively illustrated book: "Dynamics: The Geometry of Behavior," AddisonWesley 1992 authored by Ralph Abraham and Shaw. Semi cascades, also know as iterated function systems, are a recent innovation, and have been wellstudied only in one dimension (the simplest case) since about 1950. The twodimensional case is the current frontier of research. And from the computer graphcis of the leading researcher come astonishing views of the new landscape, such as the Julia and Mandelbrot sets in the beautiful books by HeinzOtto Peigen and his coworkers. Now, the new theory of critical curves developed by Mira and his students and Toulouse provide a unique opportunity to explain the basic concepts of the theory of chaos and bifurcations for discete dynamical systems in twodimensions. The materials in the book and on the accompanying disc are not solely developed only with the researcher and professional in mind, but also with consideration for the student. The book is replete with some 100 computer graphics to illustrate the material, and the CDROM contains fullcolor animations that are tied directly into the subject matter of the book, itself. In addition, much of this material has also been classtested by the authors. The crossplatform CD also contains a software program called ENDO, which enables users to create their own 2D imagery with XWindows. Maple scripts are provided which give the reader the option of working directly with the code from which the graphcs in the book were
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