Introduction to Chaotic Dynamical SystemsMath 203-A
This course is an introduction to chaotic dynamical
systems through theory and computer experimentation.
We begin by examining discrete dynamical systems,
bifurcations, and transitions to chaos. We will build up
analytic tools, including fractal geometry and a little
complex analysis to end the course with dynamics in
the complex plane, Julia sets and the Mandelbrot set.
Prerequisites: Mathematics 126.
Temporary Link to Fractals
A link to Amazon.com's website for the textbook.
We'll be using ``A first course in chaotic dynamical systems",
by Professor Robert Devaney, at Boston University.
- Week 1:
- Sep 2: Chapters 1 and 2 Homework (Turn all in)
- Sep 4: Chapter 3 (Turn in problems with an asterisk next Tuesday): 2, 3, 6, 7(b*, d*), 8, 10*
- Sep 5 (Meet in Computer Lab): We'll work on Chapter 3, Section 3.6
(The Computer May Lie), Exercise 11 , 12 (in Matlab). Also,
Chapter 4, Exercises 2(a,c) (in Matlab), problem 7 (by hand)
If you have had the Calculus Lab, here is a Maple
Worksheet with the Doubling Function
- Week 2:
- Sep 9: Be sure to look over the proofs in Chapter 5. In Chapter 5,
do problems 1(a,c,f), 2(a,d,e).
- Sep 11: Turn the solutions in for these (as discussed in class):
- Sep 12: No extra homework (Work on the stuff from last time)
- Week 3
- Sep 16:
- Sep 18 (No extra HW today):
- Sep 19: Finish Chapter 7, start Chapter 8 (Add to HW: p. 80, 1, 2, 3, 8)
- Week 4
Change in the format
Course Topics and class members
- Week 5
- Week 6
- Oct 7: Amanda presented items from 9.4
- Oct 9: Jackson introduced the concept of Chaos.
- Oct 10: Henok continued in Chapter 10.
- Week 7
- Oct 14: No Classes
- Oct 16: Continuing in Chapter 10.
Corrections to Exam 1 Due today.
Homework Set assigned today
- Oct 17: Lyapunov Exponents
- Week 8
- Oct 21: Homework problems from Ch 10 finished. (Hillary did part)
- Oct 23: Section 11.1: David
Homework: From Chapter 11: 1, 3, 4, 7. Plus:
f is piecewise linear and f(1)=2, f(2)=3 and f(3)=1, go
through the argument from class to find the intervals I_0,
I_1, A_1, A_2, A_3 and A_4 (find the intervals explicitly).
A graph will help.
- Oct 24: Section 11.2: Matthew
Homework: Read over 11.3/11.4 for Tuesday.
- Week 9
- Week 10
- Nov 4: We finished the subshifts from Chapter 11 and
Cody presented the material from 12.1.
- Nov 6: Chapter 12.2: Eric presented material from 12.2
SOLUTIONS to the Homework from Chapter 11
- Nov 7: Chapter 13
- Week 11
- Nov 11: Chapter 13 (Newton's Method)
- Nov 13 Review
- Nov 14: Exam 2 (Chapters 8-12, maybe some on 13)
- Week 12
- Nov 18: Information on Presentations
- Nov 20: Work on presentations
- Nov 21: Work on presentations
- Thanksgiving Break
- Week 13
- Dec 2: Hundley (Complex Numbers), Hillary (Intro to Fractals)
- Dec 4: Aaron and Cody: Julia Sets
- Dec 5: David and TC: The Mandelbrot Set
- Week 14
- Dec 9: Matthew (Complex Newton), Jackson (Fractals)
- Dec 11: Henok and Amanda: The Lorenz Attractor
- Dec 12: Open- Work on your papers- Due next Mon 5PM.