Chaotic Dynamics: An Introduction Based on Classical Mechanics

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Cambridge University Press, Aug 24, 2006 - Mathematics - 393 pages
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It has been discovered over the past few decades that even motions in simple systems can have complex and surprising properties. This volume provides a clear introduction to these chaotic phenomena, based on geometrical interpretations and simple arguments, without the need for prior in-depth scientific and mathematical knowledge. Richly illustrated throughout, its examples are taken from classical mechanics whose elementary laws are familiar to the reader. In order to emphasize the general features of chaos, the most important relations are also given in simple mathematical forms, independent of any mechanical interpretation.
  

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Contents

Chaotic motion
3
Fractal objects
24
Regular motion
51
Driven motion
90
Chaos in dissipative systems
113
Transient chaos in dissipative systems
191
Chaotic scattering
264
Applications of chaos
279
outlook
318
Numerical solution of ordinary differential equations
329
Solutions to the problems
343
Bibliography
370
Index
387
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