Complex Dynamics (Universitext) by Lennart Carleson (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “It gives a comprehensive account of the field…a valuable guide…” — ZENTRALBLATT MATH

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I got the Complex Dynamics book that Dr. McMullen recommended and I linked last to Amazon.com : there is no mention of programming anywhere in the book! It is Ivory tower math that enshrines the ” Julia set” as perfect mathematics, ha, ha… Since I have used IFS to simulate Julia sets experimentally, I can say that I have a hard time recognizing it in their language! Something is dreadfully wrong in this axiomatic approach that ignores the actual math that is calculated and it’s methods! The thesis on Herman’s rings by the Dane is as good a complex dynamics text as this one and he actually defines terms like quasicomformal in Riemannian terms so that it can be understood! There is a real need for better bridging books between graduate level axiomatic approaches and beginning complex variables and programming! It should probably not be written by a professor type who will be forced to bend to ” peers” in his use of language. Definition of terms and glossaries are so sadly missing in so many of these books!I amend this review years later. I’ve been using this book as a reference and studying it.I stand by the first review as it was a disappointment when I bought it, but after yearsI found that it is better than other books that I can find on the subject( specifically:

⭐).Professors in this area of computer mathematics are told not to includeprograms for some reason: it is the kiss of death to the book!You can only compute these sets with a computer program of some sort,so that a book that leaves out the programs leaves out much of the subject.I’ve been doing this for more than 20 years and still much the professors say is worthlessin actual practice.

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