# MAT 656: Transcendental Dynamics

# Spring 2014

# Christopher Bishop

Office: 4-112 Mathematics Building

Phone: (516)-632-8274

Dept. Phone: (516)-632-8290

FAX: (516)-632-7631

TuTh 11:30pm to 12:50pm, Math 4-130

I am trying to write some lecture notes to go along with
the class. You can find the current version
here ,
but they are incomplete, very rough and have no references yet.

## Introduction to the course

This is a continuation of the MAT 627 course I taught in Spring
2013, but it is not necessary to have attended the previous
course to understand this one. I will start by reviewing the
material I covered last time (without most of the proofs, but
these are included in my course notes, before starting on new
material.

The new material will start with an introduction to extremal
length and quasiconformal mappings, including (I hope) a proof
of the measurable Riemann mapping theorem. We will then cover
a variety of topics that depend on these techniques, such as:
Sullivan's non-wandering domain theorem for entire functions with
finite singular sets; the construction of entire functions
by quasiconformal folding; the construction of annular
Fatou components; the fact the maps between Fatou components
omit at most one point.

Webpage for
the previous course, MAT 627, Spring 2013. This page
gives a brief introduction to the topics covered in
both classes and links to a number of relevant papers.

Send the lecturer (C. Bishop) email at:
bishop - at - math.sunysb.edu

Send email to the whole class ((C. Bishop and students)
class list