Chaos : The Science of Predictable Random Motion (Paperback)

 Elucidates the paradox of chaotic motion
* Discusses chaotic systems without the use of calculus
* Companion CD, with point-and-click animated experiments
* Uniquely comprehensive discussion at this level
* Includes historical perspective on chaos theory

Based on only elementary mathematics, this engaging account of chaos theory bridges the gap between introductions for the layman and college-level texts. It develops the science of dynamics in terms of small time steps, describes the phenomenon of chaos through simple examples, and concludes with a close look at a homoclinic tangle, the mathematical monster at the heart of chaos. The presentation is enhanced by many figures, animations of chaotic motion (available on a companion CD), and biographical sketches of the pioneers of dynamics and chaos theory. To ensure accessibility to motivated high school students, care has been taken to explain advanced mathematical concepts simply, including exponentials and logarithms, probability, correlation, frequency analysis, fractals, and transfinite numbers. These tools help to resolve the intriguing paradox of motion that is predictable and yet random, while the final chapter explores the various ways chaos theory has been put to practical use.

Table Of Contents

1: Chaos Everywhere

2: Galileo Galilei --- Birth of a New Science

3: Isaac Newton --- Dynamics Perfected

4: Celestial Mechanics --- Clockwork Universe

5: Pendulum --- Linear and Nonlinear

6: Josephson Effect --- Synchronization

7: Chaos Forgets the Past

8: Chaos Takes a Random Walk

9: Chaos Makes Noise

10: Edward Lorenz --- Butterfly Effect

11: Chaos Comes of Age

12: Tilt-A-Whirl --- Chaos at the Amusement Park

13: Billiard-Ball Chaos --- Atomic Disorder

14: Iterated Maps --- Chaos Made Simple

15: State Space --- Going with the Flow

16: Strange Attractor

17: Fractal Geometry

18: Stephen Smale --- Horseshoe Map

19: Henri Poincare' --- Topological Tangle

20: Chaos Goes to Work