Complex Dynamics

by Lennart Carleson, Theodore W. Gamelin

A discussion of the properties of conformal mappings in the complex plane, closely related to the study of fractals and chaos. Indeed, the book ends in a detailed study of the famous Mandelbrot set, which describes very general properties of such mappings. Focusing on the analytic side of this contemporary subject, the text was developed from a course taught over several semesters and aims to help students and instructors to familiarize themselves with complex dynamics. Topics covered include: conformal and quasi-conformal mappings, fixed points and conjugations, basic rational iteration, classification of periodic components, critical points and expanding maps, some applications of conformal mappings, the local geometry of the Fatou set, and quadratic polynomials and the Mandelbrot set.

Genres: Mathematics

201 pages, Paperback

First published July 23, 1993

Reviews

[Robert · Rating 5 out of 5]

We used this in a seminar in grad school. It is a good and easy to follow introduction to complex dynamics.