MTH 445 
Introduction to Chaotic Dynamical Systems
 
TuTh 2:00-3:15 PM
White Hall 216

Instructor    Araceli Bonifant  
Office: Tyler Hall 217
Phone: 874-4394
Email: bonifant@math.uri.edu

Office Hours: Tuesday 4:00PM, Wednesday 4:00PM

Notes: Dynamics: Introductory Lectures by John Milnor
(I will provide them)

This page is subject to change according to the progress of the class.

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, Lorenz, H\'enon.

  • 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.

  • Topological Dynamics
    Basic Concepts: Periodicity and limiting behavior. Recurrence and wandering. Transitivity and minimality. Chaos: sensitive dependence, mixing. Expansiveness.

  • Attraction and Repulsion
    Attracting sets. Attractors. Repelling sets and repellors.

    • Evaluation Policy:

  • Homeworks             40%
  • 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.