A First Course in Chaotic Dynamical Systems:
Experiments with Mathematica

Robert L. Devaney & Sebastian M. Marotta

Introduction

These Mathematica notebooks are meant to accompany the book "A first course in chaotic dynamical systems" by Robert L. Devaney. In many instances it will be useful (and sometimes necessary) to read the chapters of the book related to the subjects treated here. Their main purpose is to allow the user (assumed familiar with the use of the Mathematica program) to do the Laboratory Experiments for the course MA 471 (671) of the Department of Mathematics at Boston University. The notebooks on the doubling function, the real and complex quadratic equation, and the complex exponential can also be useful for the comprehension of many of the themes related to the course. 

Note: Some of the notebooks have an Initialization cell. In general, this cell will be automatically evaluated before any other on the same notebook. In some cases (e.g. when using two notebooks in parallel) it could be necessary to evaluate them manually in order to avoid superposition on some definitions.

Real Functions:

The doubling function

Experiment: The Computer May Lie

The quadratic equation

Experiment: Rates of Convergence

Experiment: Windows in the Orbit Diagram

Experiment: Feigenbaum's Constant

Experiment: Iterated Function Systems

Complex Functions:

The quadratic equation

Experiment: Periods of the Bulbs

Experiment: Junction Points

The exponential function

Acknowledgements

We would like to thank Dan Look for his detailed review and comments.

References:

1. Robert L. Devaney. A First Course in Chaotic Dynamical Systems, Theory and Experiments. Perseus Books, 1992.
2. Ghonat Getz and Janet Helmstedt. Fractals, Patterns and Natural Forms with Mathematica. In Press. 
3. Stephen Wolfram, The Mathematica Book, 4th ed. (Wolfram Media/Cambridge University Press, 1999)
4. Wolfram Research, Mathematica 4.0 Standard Add On Packages (Wolfram Media, 1999)
5. Tom Wickham-Jones. Mathematica Graphics. Springer-Verlag, 1994.