Chaos: The Science of Predictable Random Motion

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OUP Oxford, 2011 - Mathematics - 369 pages
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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.
 

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Contents

Dynamics
17
Random motion
93
Sensitive motion
143
Topology of motion
251
Conclusion
335
Bibliography
359
Index
367
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About the author (2011)


Richard Kautz is an engineer and physicist who holds a doctorate from the Massachusetts Institute of Technology. During his career at the National Institute of Standards and Technology, he helped develop fundamental quantum standards for both voltage and capacitance. Kautz is a Fellow of the American Physical Society and a recipient of the Samuel Stratton Award for measurement science and the Edward Condon Award for scientific writing.