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.
Iterates of Functions
Families of Functions
The Quadratic Family
The Schwarzian Derivative
Transitivity and Strong Chaos
Review of Matrices
Dynamics of Linear Functions
The Hénon Map
The Horseshoe Map
Systems of Differential Equations
Review of Systems of Differential Equations
The Lorenz System
Introduction to Fractals
The Sierpiński Gasket and Other "Monsters"
Similarity and Capacity Dimensions
Calculating Fractal Dimensions of Objects
Creating Fractals Sets
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
The Mandelbrot Set
Answers to Selected Exercises