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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Chaotic Contact BifurcationsChaotic contact bifurcations involve a chaotic attractor. This is the pinnacle of our subject. Here we proceed with a 1D introduction, and a 2D introduction, before analyzing the exemplary bifurcation sequence.

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Fractal Boundariesrcations, 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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Conclusiontractors, 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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Book 1997 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

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Book 1997systems), 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 Beh

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