Chaos: An Introduction to Dynamical Systems

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Springer Science & Business Media, 1997 - Mathematics - 603 pages
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Chaos: An Introduction to Dynamical Systems, was developed and class-tested by a distinguished team of authors at two universities through their teaching of courses based on the material. Intended for courses in nonlinear dynamics offered either in Mathematics or Physics, the text requires only calculus, differential equations, and linear algebra as prerequisites. Along with discussions of the major topics, including discrete dynamical systems, chaos, fractals, nonlinear differential equations and bifurcations, the text also includes Lab Visits, short reports that illustrate relevant concepts from the physical, chemical and biological sciences. There are Computer Experiments throughout the text that present opportunities to explore dynamics through computer simulations, designed to be used with any software package. And each chapter ends with a Challenge, which provides students a tour through an advanced topic in the form of an extended exercise.
  

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Contents

INTRODUCTION
1
TWODIMENSIONAL MAPS
43
CHAOS
105
FRACTALS
149
CHAOS IN TWODIMENSIONAL MAPS
193
CHAOTIC ATTRACTORS
231
DIFFERENTIAL EQUATIONS
273
PERIODIC ORBITS AND LIMIT SETS
329
BIFURCATIONS
447
CASCADES
499
STATE RECONSTRUCTION FROM DATA
537
A MATRIX ALGEBRA
557
B COMPUTER SOLUTION OF ODES
567
ANSWERS AND HINTS TO SELECTED EXERCISES
577
BIBLIOGRAPHY
587
INDEX
595

CHAOS IN DIFFERENTIAL EQUATIONS
359
STABLE MANIFOLDS AND CRISES
399

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About the author (1997)

Yorke is Distinguished Professor of Mathematics and Director, the Institute for Physical Sciences and Technology, at the University of Maryland, USA. He was awarded the Guggenheim Fellowship in 1980 and is widely known as the coiner of the term "chaos".

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