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Author: Daniel S. Alexander Publisher: American Mathematical Soc. ISBN: 0821844644 Category : Mathematics Languages : en Pages : 474
Book Description
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.
Author: Daniel S. Alexander Publisher: American Mathematical Soc. ISBN: 0821844644 Category : Mathematics Languages : en Pages : 474
Book Description
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.
Author: Daniel S. Alexander Publisher: Springer Science & Business Media ISBN: 366309197X Category : Technology & Engineering Languages : en Pages : 175
Book Description
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.
Author: Lennart Carleson Publisher: Springer Science & Business Media ISBN: 1461243645 Category : Mathematics Languages : en Pages : 181
Book 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.
Author: Dierk Schleicher Publisher: CRC Press ISBN: 1439865426 Category : Mathematics Languages : en Pages : 663
Book Description
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
Author: John Milnor Publisher: Princeton University Press ISBN: 1400835534 Category : Mathematics Languages : en Pages : 313
Book Description
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.
Author: Yaneer Bar-yam Publisher: CRC Press ISBN: 0429717598 Category : Mathematics Languages : en Pages : 866
Book Description
This book aims to develop models and modeling techniques that are useful when applied to all complex systems. It adopts both analytic tools and computer simulation. The book is intended for students and researchers with a variety of backgrounds.
Author: Robert L. Devaney Publisher: American Mathematical Soc. ISBN: 0821836250 Category : Mathematics Languages : en Pages : 218
Book Description
Chaotic behavior of (even the simplest) iterations of polynomial maps of the complex plane was known for almost one hundred years due to the pioneering work of Farou, Julia, and their contemporaries. However, it was only twenty-five years ago that the first computer generated images illustrating properties of iterations of quadratic maps appeared. These images of the so-called Mandelbrot and Julia sets immediately resulted in a strong resurgence of interest in complex dynamics. The present volume, based on the talks at the conference commemorating the twenty-fifth anniversary of the appearance of Mandelbrot sets, provides a panorama of current research in this truly fascinating area of mathematics.
Author: Wolfgang Götze Publisher: Oxford University Press on Demand ISBN: 0199235341 Category : Science Languages : en Pages : 654
Book Description
Amorphous condensed matter can exhibit complex motions on time scales which extend up to those relevant for the functioning of biomaterials. The book presents the derivation of a microscopic theory for amorphous matter, which exhibits the evolution of such complex motions as a new paradigm of strongly interacting particle systems.e
Author: Daniel S. Alexander
Author: Daniel S. Alexander
Author: Daniel S. Alexander
Author: Daniel S. Alexander
Author: Lennart Carleson
Author: Dierk Schleicher
Author: John Milnor
Author: Yaneer Bar-yam
Author: Daniel S. Alexander
Author: Robert L. Devaney
Author: Wolfgang Götze