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Titlebook: Chaos in Discrete Dynamical Systems; A Visual Introductio Ralph H. Abraham,Laura Gardini,Christian Mira Book 1997 Springer Science+Business

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书目名称Chaos in Discrete Dynamical Systems
副标题A Visual Introductio
编辑Ralph H. Abraham,Laura Gardini,Christian Mira
视频video
图书封面Titlebook: Chaos in Discrete Dynamical Systems; A Visual Introductio Ralph H. Abraham,Laura Gardini,Christian Mira Book 1997 Springer Science+Business
描述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 semi-cascades (discrete, irreversible, dynamical systems). Flows and semi-cascades are the classical systems iuntroduced by Poincare a centry ago, and are the subject of the extensively illustrated book: "Dynamics: The Geometry of Behavior," Addison-Wesley 1992 authored by Ralph Abraham and Shaw. Semi- cascades, also know as iterated function systems, are a recent innovation, and have been well-studied only in one dimension (the simplest case) since about 1950. The two-dimensional 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 Heinz-Otto Peigen and his co-workers. Now, the new theory of critical curves developed byMira 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 two-dimensions. The materials in t
出版日期Book 1997
关键词Chaos; Maple; calculus; chaos theory; computer graphics; dynamische Systeme; geometry; linear optimization;
版次1
doihttps://doi.org/10.1007/978-1-4612-1936-1
isbn_softcover978-1-4612-7347-9
isbn_ebook978-1-4612-1936-1
copyrightSpringer Science+Business Media New York 1997
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https://doi.org/10.1007/978-3-662-47224-8rcations, which we have encountered already in Chapter 5, with a sequence of hand drawings. Then we will go on to an exemplary bifurcation sequence with computer graphics, in which the fractal implications of these contact events for the boundaries become clear.
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https://doi.org/10.1007/978-3-662-47224-8tractors, basins, critical sets, bifurcations, and so on — may be understood in the 1D context, as we have indicated here and there; but perhaps they are clearer in 2D. Also, the 2D versions may admit a more straightforward generalization to 3D and higher dimensions.
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https://doi.org/10.1007/978-3-662-47224-8s ideal) and few mathematical symbols.. We illustrate all the basic ideas with hand drawings and monochrome computer graphics in the book, and again with movies (full-motion video animations in color) on the companion CD-ROM.
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M. P. Dobhal,V. Gupta,M. D. Lechner,R. Gupta which is our main concern in this book. We no longer have the convenience of a visible graph of the map, however, because the graph of a 2D map is a 2D surface in a 4D space. Therefore, we must be satisfied with a frontal view of the 2D domain of the map, in which we try to visualize as much as possible.
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