Seminar on Chaos and Fractals

Organizers: Dr. Palagallo (palagallo at uakron dot edu) and Dr. Adler (adler at uakron dot edu)

Time: Spring, 1999, Thursdays 11-12 am.

Prerequisite: Calculus II, Calculus I Honors, or permission.

In this one-credit seminar, we will explore some basic topics of discrete dynamical systems and fractal geometry. In addition to performing mathematical exercises, participants will experiment with software that demonstrates both chaotic behavior and the generation of fractal images.

The seminar is especially designed to be accessible to undergraduates as well as graduates. Enroll for credit by using the 3450:489/589 topics number. The last date to withdraw from the course is April 16, 1999.

If you have questions, please contact either of the organizers.

Here are some useful links.

Outline of topics:

1. Basic examples of discrete dynamical systems
2. Orbits
3. Graphical analysis
4. Attracting and repelling cycles
5. Bifurcation
6. Symbolic dynamics
7. Definition of chaos
8. Definition and examples of fractal curves
9. The chaos game
10. Random iteration
11. Affine transformations
12. The Mandelbrot set and Julia sets

• Robert L. Devaney, Chaos, Fractals, and Dynamics, Perseus, 1990.
• Robert L. Devaney, A First Course in Chaotic Dynamical Systems, Perseus, 1992.
• Richard M. Crownover, Introduction to Fractals and Chaos, Jones and Bartlett, 1995.
• H. Lauwerier, Fractals, Princeton University Press, 1991.