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.
Complex Dynamics
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"It gives a comprehensive account of the field...a valuable guide..." -- ZENTRALBLATT MATH
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3 of 44 people found the following review helpful:
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By R. Bagula "Roger L. Bagula" (Lakeside, Ca United States) - See all my reviews (VINE VOICE) (REAL NAME)
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This review is from: Complex Dynamics (Universitext / Universitext: Tracts in Mathematics) (Paperback)
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!
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Inside This Book
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First Sentence:
We discuss some topics that are not included in the standard introductory graduate course in complex analysis. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nonrepelling cycles, repelling arm, attracting petal, parabolic cycle, completely invariant components, postcritical set, superattracting fixed point, parabolic periodic point, ellipse field, quasiconformal surgery, superattracting cycle, parabolic fixed point, neutral cycles, neutral fixed points, inverse iterates, main cardioid, immediate basin, external rays, attracting periodic point, repelling fixed point, attracting cycles, repelling periodic point, hyperbolic components, infinitesimal circles, distortion theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Homeomorphisms of the Circle New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
We discuss some topics that are not included in the standard introductory graduate course in complex analysis. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nonrepelling cycles, repelling arm, attracting petal, parabolic cycle, completely invariant components, postcritical set, superattracting fixed point, parabolic periodic point, ellipse field, quasiconformal surgery, superattracting cycle, parabolic fixed point, neutral cycles, neutral fixed points, inverse iterates, main cardioid, immediate basin, external rays, attracting periodic point, repelling fixed point, attracting cycles, repelling periodic point, hyperbolic components, infinitesimal circles, distortion theorem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Homeomorphisms of the Circle New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 62
books:
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100
books
cite this book:
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- Computer Graphics by Acm Press in Back Matter (1), and Back Matter (2)
- Complex Analysis: The Argument Principle in Analysis and Topology by A.F. Beardon in Back Matter (1), and Back Matter (2)
- The Science of Fractal Images by Heinz-Otto Peitgen in Back Matter (1), and Back Matter (2)
- Chaos and Fractals: The Mathematics Behind the Computer Graphics (Proceedings of Symposia in Applied Mathematics) by Robert L. Devaney in Back Matter (1), and Back Matter (2)
- Introduction to Algebra (Universitext) by A.I. Kostrikin in Front Matter
See all 62 books this book cites
- Progress in Holomorphic Dynamics (Chapman & Hall/CRC Research Notes in Mathematics Series) by Hartje Kriete on page 30, and page 39
- Dimension Theory in Dynamical Systems: Contemporary Views and Applications (Chicago Lectures in Mathematics) by Yakov B. Pesin in Back Matter
- Theory and Numerics of Differential Equations by James F. Blowey in Back Matter
- Finite or Infinite Dimensional Complex Analysis (Lecture Notes in Pure and Applied Mathematics) by Joji Kajiwara on page 589
- Logic and Structure by Dirk van Dalen in Back Matter
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