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Complex Dynamics

2013-11-11 Mathematics
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Release : 2013-11-11
Genre : Mathematics
Kind : eBook
Book Rating : 645/5 ( reviews)

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Book Synopsis Complex Dynamics by : Lennart Carleson

Download or read book Complex Dynamics written by Lennart Carleson. This book was released on 2013-11-11. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A History of Complex Dynamics

2013-06-29 Technology & Engineering
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Release : 2013-06-29
Genre : Technology & Engineering
Kind : eBook
Book Rating : 97X/5 ( reviews)

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Book Synopsis A History of Complex Dynamics by : Daniel S. Alexander

Download or read book A History of Complex Dynamics written by Daniel S. Alexander. This book was released on 2013-06-29. Available in PDF, EPUB and Kindle. Book excerpt: The contemporary study of complex dynamics, which has flourished so much in recent years, is based largely upon work by G. Julia (1918) and P. Fatou (1919/20). The goal of this book is to analyze this work from an historical perspective and show in detail, how it grew out of a corpus regarding the iteration of complex analytic functions. This began with investigations by E. Schröder (1870/71) which he made, when he studied Newton's method. In the 1880's, Gabriel Koenigs fashioned this study into a rigorous body of work and, thereby, influenced a lot the subsequent development. But only, when Fatou and Julia applied set theory as well as Paul Montel's theory of normal families, it was possible to develop a global approach to the iteration of rational maps. This book shows, how this intriguing piece of modern mathematics became reality.

Complex Dynamics and Renormalization

1994-12-19 Mathematics
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Release : 1994-12-19
Genre : Mathematics
Kind : eBook
Book Rating : 818/5 ( reviews)

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Book Synopsis Complex Dynamics and Renormalization by : Curtis T. McMullen

Download or read book Complex Dynamics and Renormalization written by Curtis T. McMullen. This book was released on 1994-12-19. Available in PDF, EPUB and Kindle. Book excerpt: Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set. The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps.

Complex Dynamics

2009-11-03 Mathematics
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Release : 2009-11-03
Genre : Mathematics
Kind : eBook
Book Rating : 426/5 ( reviews)

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Book Synopsis Complex Dynamics by : Dierk Schleicher

Download or read book Complex Dynamics written by Dierk Schleicher. This book was released on 2009-11-03. Available in PDF, EPUB and Kindle. Book excerpt: Complex Dynamics: Families and Friends features contributions by many of the leading mathematicians in the field, such as Mikhail Lyubich, John Milnor, Mitsuhiro Shishikura, and William Thurston. Some of the chapters, including an introduction by Thurston to the general subject of complex dynamics, are classic manuscripts that were never published

Dynamics in One Complex Variable

2011-02-11 Mathematics
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Release : 2011-02-11
Genre : Mathematics
Kind : eBook
Book Rating : 534/5 ( reviews)

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Book Synopsis Dynamics in One Complex Variable by : John Milnor

Download or read book Dynamics in One Complex Variable written by John Milnor. This book was released on 2011-02-11. Available in PDF, EPUB and Kindle. Book excerpt: This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the écalle-Voronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated. Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field.

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