| Anthony G. O'Farrell: MT522 Complex Dynamical Systems |
We assume a knowledge of elementary complex analysis, and some competence with a symbolic manipulator and a programming language. I'll begin by explaining further background material in complex analysis, including material about univalent functions, uniformization, and the Riemann-Hurwicz formula. I'll also cover the basics of quasiconformal mappings and singular integral operators.
The course will approximate to the first half or so of Carleson & Gamelin's book on Complex Dynamics, which I recommend you buy. We will go as far as Sullivan's theorem on non-wandering domains.
You will have the opportunity to do some
practical work, using Maple ond/or a language of
your choice. There will also be theoretical homework
to do.
Other References:
D.S. Alexander. A History of Complex Dynamics from Schroeder to Fatou and
Julia. Vieweg. 1994. 515.9 ALE
Nice book, using minimal technicality, with many interesting facts.
Makes the case that functional equations, rather than mechanical systems,
provided the main initial impetus for the development of holomorphic
iteration theory.
J. Milnor. Dynamics in One Complex Variable. 2nd ed. Vieweg. 2000.
515.93 MIL.
The master speaks. Wonderful book. Full of insight.
Skips technical background stuff
and gives the bird's-eye view.
N. Steinmetz. Rational Iteration. de Guyter. 1993. 515.9 STE.
Careful and thorough account, proving everything.
R.L. Devaney. An intro to Chaotic Dynamical Systems. Addison-Wesley. 1989.
The first modern book about the subject. Keeps the prerequisites minimal.
Useful place to start.