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Encounters with Chaos and Fractals

Denny Gulick
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2012
Number of Pages: 
371
Format: 
Hardcover
Edition: 
2
Price: 
79.95
ISBN: 
9781584885177
Category: 
Textbook
[Reviewed by
Fernando Q. Gouvêa
, on
02/14/2013
]

The Telegraphic Review of the first edition, in the February 1993 issue of the American Mathematical Monthly, described this book as an

Accessible post-calculus introduction to the central ideas and techniques of dynamical systems. Two chapters analyzing the standard one-dimensional examples. One chapter each on two-dimensional examples (Hénon, horseshoe), fractals, and differential equations. TRUE Basic computer programs; plenty of exercises.

The second edition has many new graphics and diagrams. The computer programs are now in Matlab. The book can be used as a textbook for an undergraduate course.


Fernando Q. Gouvêa is the Editor of MAA Reviews.

Periodic Points
Iterates of Functions
Fixed Points
Periodic Points
Families of Functions
The Quadratic Family
Bifurcations
Period-3 Points
The Schwarzian Derivative

One-Dimensional Chaos
Chaos
Transitivity and Strong Chaos
Conjugacy
Cantor Sets

Two-Dimensional Chaos
Review of Matrices
Dynamics of Linear Functions
Nonlinear Maps
The Hénon Map
The Horseshoe Map

Systems of Differential Equations
Review of Systems of Differential Equations
Almost Linearity
The Pendulum
The Lorenz System

Introduction to Fractals
Self-Similarity
The Sierpiński Gasket and Other "Monsters"
Space-Filling Curves
Similarity and Capacity Dimensions
Lyapunov Dimension
Calculating Fractal Dimensions of Objects

Creating Fractals Sets
Metric Spaces
The Hausdorff Metric
Contractions and Affine Functions
Iterated Function Systems
Algorithms for Drawing Fractals

Complex Fractals: Julia Sets and the Mandelbrot Set
Complex Numbers and Functions
Julia Sets
The Mandelbrot Set

Computer Programs

Answers to Selected Exercises

References

Index

 

Dummy View - NOT TO BE DELETED