Chaos and Fractals: An Elementary Introduction

Paperback | September 2, 2012

byDavid P. Feldman

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This book provides the reader with an elementary introduction to chaos and fractals, suitable for students with a background in elementary algebra, without assuming prior coursework in calculus or physics. It introduces the key phenomena of chaos - aperiodicity, sensitive dependence on initialconditions, bifurcations - via simple iterated functions. Fractals are introduced as self-similar geometric objects and analyzed with the self-similarity and box-counting dimensions. After a brief discussion of power laws, subsequent chapters explore Julia Sets and the Mandelbrot Set. The last partof the book examines two-dimensional dynamical systems, strange attractors, cellular automata, and chaotic differential equations.The book is richly illustrated and includes over 200 end-of-chapter exercises. A flexible format and a clear and succinct writing style make it a good choice for introductory courses in chaos and fractals.

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This book provides the reader with an elementary introduction to chaos and fractals, suitable for students with a background in elementary algebra, without assuming prior coursework in calculus or physics. It introduces the key phenomena of chaos - aperiodicity, sensitive dependence on initialconditions, bifurcations - via simple itera...

David Feldman joined the faculty at College of the Atlantic in 1998, having completed a PhD in Physics at the University of California. He served as Associate Dean for Academic Affairs from 2003 - 2007. At COA Feldman has taught over twenty different courses in physics, mathematics, and computer science. Feldman's research interests li...

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Format:PaperbackDimensions:448 pages, 9.69 × 7.44 × 0.68 inPublished:September 2, 2012Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199566445

ISBN - 13:9780199566440

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Table of Contents

I. Introducing Discrete Dynamical SystemsOpening Remarks1. Functions2. Iterating Functions3. Qualitative Dynamics4. Time Series Plots5. Graphical Iteration6. Iterating Linear Functions7. Population Models8. Newton, Laplace, and DeterminismII. Chaos9. Chaos and the Logistic Equation10. The Buttery Effect11. The Bifurcation Diagram12. Universality13. Statistical Stability of Chaos14. Determinism, Randomness, and NonlinearityIII. Fractals15. Introducing Fractals16. Dimensions17. Random Fractals18. The Box-Counting Dimension19. When do Averages exist?20. Power Laws and Long Tails20. Introducing Julia Sets21. Infinities, Big and SmallIV. Julia Sets and The Mandelbrot Set22. Introducing Julia Sets23. Complex Numbers24. Julia Sets for f(z) = z2 + c25. The Mandelbrot SetV. Higher-Dimensional Systems26. Two-Dimensional Discrete Dynamical Systems27. Cellular Automata28. Introduction to Differential Equations29. One-Dimensional Differential Equations30. Two-Dimensional Differential Equations31. Chaotic Differential Equations and Strange AttractorsVI. Conclusion32. ConclusionVII. AppendicesA. Review of Selected Topics from AlgebraB. Histograms and DistributionsC. Suggestions for Further Reading

Editorial Reviews

"David P. Feldman provides a delightful and thoughtful introduction to chaos and fractals requiring only a good background in algebra. The formal treatment of nonlinear dynamics, chaotic behavior, Lyapunov exponents, and fractal dimensions is leavened with creative analogies and many helpfuland visually attractive figures and diagrams. Even more mathematically sophisticated readers will find this book a good starting point in exploring the complex and beguiling realms of chaos and fractals." --Robert C. Hilborn, Associate Executive Officer, American Association of Physics Teachers