Complex dynamics
By: Lennart Carleson, Theodore W. Gamelin.
Contributors: Gamelin, Theodore W.
Series: Universitext.
Publisher: Springer-Verlag
Published: 1993
Place of publication: New York
Language: eng
Number of pages: 174
Subjects: Functions of complex variables; Mappings (Mathematics); Fixed point theory
Description: "Complex Dynamics discusses the properties of conformal mappings in the complex plane, a subject that is closely connected to the study of fractals and chaos. Indeed the culmination of the book is a detailed study of the famous Mandelbrot set, which describes very general properties of such mappings. The book focuses on the analytic side of this contemporary subject. The text was developed out of a course taught over several semesters; its focus is 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 (the Julia set), classification of periodic components, critical points and expanding maps, some applications of conformal mappings (e.g. Hermann rings), the local geometry of the Fatou set, and quadratic polynomials and the Mandelbrot set"--Publisher description.
Notes: Includes bibliographical references (p. [163]-170) and indexes.
"Based on lectures of the first author at UCLA over several winter quarters, particularly 1986 and 1990"--Pref.