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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.

A History of Complex Dynamics

2014-01-15
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Release : 2014-01-15
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Kind : eBook
Book Rating : 981/5 ( 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 2014-01-15. Available in PDF, EPUB and Kindle. Book excerpt:

Early Days in Complex Dynamics

2012 Mathematics
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Release : 2012
Genre : Mathematics
Kind : eBook
Book Rating : 644/5 ( reviews)

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Book Synopsis Early Days in Complex Dynamics by : Daniel S. Alexander

Download or read book Early Days in Complex Dynamics written by Daniel S. Alexander. This book was released on 2012. Available in PDF, EPUB and Kindle. Book excerpt: The theory of complex dynamics, whose roots lie in 19th-century studies of the iteration of complex function conducted by Koenigs, Schoder, and others, flourished remarkably during the first half of the 20th century, when many of the central ideas and techniques of the subject developed. This book paints a robust picture of the field of complex dynamics between 1906 and 1942 through detailed discussions of the work of Fatou, Julia, Siegel, and several others.

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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