Chaos and Fractals: An Elementary Introduction

by David P. Feldman

Overview

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 initial conditions, 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 part of 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.

To request a copy of the Solutions Manual, visit: http://global.oup.com/uk/academic/physics/admin/solutions

Product Details

ISBN-13:	9780199566440
Publisher:	Oxford University Press
Publication date:	10/12/2012
Edition description:	New Edition
Pages:	432
Product dimensions:	9.60(w) x 7.40(h) x 0.90(d)

About the Author

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 lie in the fields of statistical mechanics and nonlinear dynamics. In his research, he uses both analytic and computational techniques. Feldman has authored research papers in journals including Physical Review E, Chaos, and Advances in Complex Systems. He has recently begun a research project looking at trends in extreme precipitation events in Maine.

Table of Contents

I. Introducing Discrete Dynamical Systems0. Opening 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

"For the right audience and instructor, this is a wonderful book. With considerable effort on both sides it can take a wide audience with modest mathematics to a reasonable understanding of what is behind much of the complex phenomena seen in modern mathematical models of the physical universe."
— Thomas B. Ward, Durham University

"There is a great deal to like about this book, starting with the author's writing style, which I found particularly clear and enjoyable. ... All in all, this is a very valuable book. ... This is an excellent book and is highly recommended." —Mark Hunacek, MAA Reviews

From the Publisher