Introduction to Complex Dynamics Winter 2022

Instructor: Danny Calegari

Eckhart 207A MWF 12:30-1:20

Description of course:

This class is an introduction to complex dynamics. We shall discuss the structure of the Fatou and Julia sets and their classification, and then move on to more specialized topics.

Cancellations:

None yet.

Notices:

The first two weeks of classes will be online. The link to these classes will be via the Canvas site for the class.

Syllabus:

• Fatou and Julia Sets
• Classification of pre-periodic domains
• No wandering domains
• Examples
• Post-critically finite maps
• The Mandelbrot set

Lectures

Notes from class:

Notes for this class will be posted online here and updated as we go along.

References:

The main references are:

• Alan Beardon, Iteration of Rational Functions Springer GTM 132
• Dennis Sullivan, Quasiconformal homeomorphisms and dynamics. I. Solution of the Fatou-Julia problem on wandering domains Ann. Math (2) 122 (1985), no. 3, 401--418