Download E-books Chaotic Maps: Dynamics, Fractals, and Rapid Fluctuations (Synthesis Lectures on Mathematics and Statistics) PDF

By Yu Huang

This booklet contains lecture notes for a semester-long introductory graduate direction on dynamical platforms and chaos taught by means of the authors at Texas A&M collage and Zhongshan collage, China. There are ten chapters normally physique of the booklet, masking an uncomplicated conception of chaotic maps in finite-dimensional areas. the themes contain one-dimensional dynamical structures (interval maps), bifurcations, normal topological, symbolic dynamical structures, fractals and a category of infinite-dimensional dynamical platforms that are prompted by way of period maps, plus swift fluctuations of chaotic maps as a brand new standpoint constructed via the authors lately. appendices also are supplied so that it will ease the transitions for the readership from discrete-time dynamical structures to continuous-time dynamical structures, ruled by way of usual and partial differential equations.

desk of Contents: basic period Maps and Their Iterations / overall diversifications of Iterates of Maps / Ordering between classes: The Sharkovski Theorem / Bifurcation Theorems for Maps / Homoclinicity. Lyapunoff Exponents / Symbolic Dynamics, Conjugacy and Shift Invariant units / The Smale Horseshoe / Fractals / speedy Fluctuations of Chaotic Maps on RN / Infinite-dimensional platforms precipitated by means of Continuous-Time distinction Equations

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