Introduction to Chaotic Dynamical Systems
TuTh 2:00-3:15 PM
White Hall 216
Office: Tyler Hall 217
Office Hours: Tuesday 4:00PM, Wednesday 4:00PM
Notes: Dynamics: Introductory Lectures by John Milnor
This page is subject to change according to the progress
of the class.
(I will provide them)
About the course:
We will cover (if time permits):
Review of some mathematical concepts needed in the course.
Chaotic Dynamics: Some History
Celestial Mechanics, Poincar\'e and sensitive dependence. The restricted
3-body problem: continuous versus discrete time. Chaotic attractors: Ueda,
The Simplest Chaotic Systems
Two maps of the interval. Angle doubling: the squaring map on the circle.
Sensitive Dependence. Symbolic dynamics: the one-sided 2 shift. The solenoid.
Basic Concepts: Periodicity and limiting behavior. Recurrence and
wandering. Transitivity and minimality. Chaos: sensitive dependence, mixing.
Attraction and Repulsion
Attracting sets. Attractors. Repelling sets and repellors.
Midterm Exam 20 %
Final Exam 20 %
Projects 20 %
Suggested Reading: (not required)
An Introduction to Chaotic Dynamical Systems, Second Edition by
Robert Devaney, Addison Wesley.