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Rotation Sets and Complex Dynamics

2018-06-23 Mathematics
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Release : 2018-06-23
Genre : Mathematics
Kind : eBook
Book Rating : 108/5 ( reviews)

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Book Synopsis Rotation Sets and Complex Dynamics by : Saeed Zakeri

Download or read book Rotation Sets and Complex Dynamics written by Saeed Zakeri. This book was released on 2018-06-23. Available in PDF, EPUB and Kindle. Book excerpt: This monograph examines rotation sets under the multiplication by d (mod 1) map and their relation to degree d polynomial maps of the complex plane. These sets are higher-degree analogs of the corresponding sets under the angle-doubling map of the circle, which played a key role in Douady and Hubbard's work on the quadratic family and the Mandelbrot set. Presenting the first systematic study of rotation sets, treating both rational and irrational cases in a unified fashion, the text includes several new results on their structure, their gap dynamics, maximal and minimal sets, rigidity, and continuous dependence on parameters. This abstract material is supplemented by concrete examples which explain how rotation sets arise in the dynamical plane of complex polynomial maps and how suitable parameter spaces of such polynomials provide a complete catalog of all such sets of a given degree. As a main illustration, the link between rotation sets of degree 3 and one-dimensional families of cubic polynomials with a persistent indifferent fixed point is outlined. The monograph will benefit graduate students as well as researchers in the area of holomorphic dynamics and related fields.

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.

Frontiers in Complex Dynamics

2014-03-16 Mathematics
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Release : 2014-03-16
Genre : Mathematics
Kind : eBook
Book Rating : 297/5 ( reviews)

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Book Synopsis Frontiers in Complex Dynamics by : Araceli Bonifant

Download or read book Frontiers in Complex Dynamics written by Araceli Bonifant. This book was released on 2014-03-16. Available in PDF, EPUB and Kindle. Book excerpt: John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing. This collection will be useful to students and researchers for decades to come. The contributors are Marco Abate, Marco Arizzi, Alexander Blokh, Thierry Bousch, Xavier Buff, Serge Cantat, Tao Chen, Robert Devaney, Alexandre Dezotti, Tien-Cuong Dinh, Romain Dujardin, Hugo García-Compeán, William Goldman, Rotislav Grigorchuk, John Hubbard, Yunping Jiang, Linda Keen, Jan Kiwi, Genadi Levin, Daniel Meyer, John Milnor, Carlos Moreira, Vincente Muñoz, Viet-Anh Nguyên, Lex Oversteegen, Ricardo Pérez-Marco, Ross Ptacek, Jasmin Raissy, Pascale Roesch, Roberto Santos-Silva, Dierk Schleicher, Nessim Sibony, Daniel Smania, Tan Lei, William Thurston, Vladlen Timorin, Sebastian van Strien, and Alberto Verjovsky.

Complex Dynamics

2006 Mathematics
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Release : 2006
Genre : Mathematics
Kind : eBook
Book Rating : 250/5 ( reviews)

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Book Synopsis Complex Dynamics by : Robert L. Devaney

Download or read book Complex Dynamics written by Robert L. Devaney. This book was released on 2006. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

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