Math 189A, Complex Dynamics, is a new half course at HMC; it will run
for the first time in the second half of Spring 2001. The course meets
on MW at 2:45pm, and lectures will run from Monday 5 March to
Wednesday 2 May. The text is *Iteration of Rational Functions*, by
Alan F. Beardon; it is available at Huntley.

The course is about the

We will study fixed points and periodic points, and their attracting, repelling, or neutral nature. We will discuss the structure and properties of the Fatou and Julia sets. For example, the repelling periodic points of a given rational mapping are dense in the Julia set, and the Julia set can also be generated as the set of accumulation points of the backwards orbit of a generic point in the Fatou set. Other topics include critical points, conjugacy, equicontinuity, and normal families of maps. We will also study the

- Mondays 10am -- noon, Olin 1281
- Tuesdays 10 -- 11am, Olin 1281

Due in class on Wednesdays. Available here in postscript format:

- Homework 1 Due Tues 20 March. Julia and Fatou sets, periodic points, conjugation.
- Homework 2
Due Wed 28 March.
Rational maps, and the iteration of z -> z
^{2}. - Homework 3
Due Tues 3 April.
Iteration of z -> z
^{2}+ c. - Homework 4 Due Wed 11 April. Prepare presentation on article.
- Homework 5 Due Wed 18 April. Fatou and Julia sets, equicontinuity, normal families.

- 60% for Homework: weekly, due on Wednesdays in class.
- 10% for First Project and report.
- 30% for Second Project and report.

Last modified April 13, 2001, by Prof Lesley Ward. ward@math.hmc.edu

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*Last modified: April 2001