Discrete chaos : with applications in science and engineering
 Author/Creator
 Elaydi, Saber, 1943
 Language
 English.
 Edition
 2nd ed.
 Imprint
 Boca Raton : Chapman & Hall/CRC, c2008.
 Physical description
 xx, 419 p. : ill. ; 25 cm. + 1 CDROM (4 3/4 in.)
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 Library has: 1 v. + 1 CD
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QA614.8 .E53 2008
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 389395) and index.
 Contents

 PREFACE FOREWORD The Stability of OneDimensional Maps Introduction Maps vs. Difference Equations Maps vs. Differential Equations Linear Maps/Difference Equations Fixed (Equilibrium) Points Graphical Iteration and Stability Criteria for Stability Periodic Points and Their Stability The PeriodDoubling Route to Chaos Applications Attraction and Bifurcation Introduction Basin of Attraction of Fixed Points Basin of Attraction of Periodic Orbits Singer's Theorem Bifurcation Sharkovsky's Theorem The Lorenz Map PeriodDoubling in the Real World Poincare Section/Map Appendix Chaos in One Dimension Introduction Density of the Set of Periodic Points Transitivity Sensitive Dependence Definition of Chaos Cantor Sets Symbolic Dynamics Conjugacy Other Notions of Chaos Rossler's Attractor Saturn's Rings Stability of TwoDimensional Maps Linear Maps vs. Linear Systems Computing An Fundamental Set of Solutions SecondOrder Difference Equations Phase Space Diagrams Stability Notions Stability of Linear Systems The TraceDeterminant Plane Liapunov Functions for Nonlinear Maps Linear Systems Revisited Stability via Linearization Applications Appendix Bifurcation and Chaos in Two Dimensions Center Manifolds Bifurcation Hyperbolic Anosov Toral Automorphism Symbolic Dynamics The Horseshoe and Henon Maps A Case Study: Extinction and Sustainability in Ancient Civilizations Appendix Fractals Examples of Fractals LSystem The Dimension of a Fractal Iterated Function System Mathematical Foundation of Fractals The Collage Theorem and Image Compression The Julia and Mandelbrot Sets Introduction Mapping by Functions on the Complex Domain The Riemann Sphere The Julia Set Topological Properties of the Julia Set Newton's Method in the Complex Plane The Mandelbrot Set Bibliography Answers to Selected Problems Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 While maintaining the lucidity of the first edition, Discrete Chaos, Second Edition: With Applications in Science and Engineering now includes many recent results on global stability, bifurcation, chaos, and fractals. The first five chapters provide the most comprehensive material on discrete dynamical systems, including tracedeterminant stability, bifurcation analysis, and the detailed analysis of the center manifold theory. This edition also covers Lsystems and the periodic structure of the bulbs in the Mandelbrot set as well as new applications in biology, chemistry, and physics. The principal improvements to this book are the additions of PHASER software on an accompanying CDROM and the Maple(t) and Mathematica(R) code available for download online. Incorporating numerous new topics and technology not found in similar texts, Discrete Chaos, Second Edition presents a thorough, uptodate treatment of the theory and applications of discrete dynamical systems.
(source: Nielsen Book Data)  Supplemental links
 Table of contents only
Bibliographic information
 Publication date
 2008
 Responsibility
 Saber N. Elaydi.
 ISBN
 9781584885924
 1584885920