Rotation Sets And Complex Dynamics

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Rotation Sets And Complex Dynamics

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Author : Saeed Zakeri
language : en
Publisher: Springer
Release Date : 2018-06-23

Rotation Sets And Complex Dynamics written by Saeed Zakeri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-23 with Mathematics categories.

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.

Frontiers In Complex Dynamics

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Author : Araceli Bonifant
language : en
Publisher: Princeton University Press
Release Date : 2014-03-16

Frontiers In Complex Dynamics written by Araceli Bonifant and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-16 with Mathematics categories.

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 Dynamical Systems The Mathematics Behind The Mandelbrot And Julia Sets

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Author : Robert L. Devaney
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

Complex Dynamical Systems The Mathematics Behind The Mandelbrot And Julia Sets written by Robert L. Devaney and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

The Mandelbrot set has emerged as one of the most recognizable objects in mathematics. While there is no question of its beauty, relatively few people appreciate the fact that the mathematics behind such images is equally beautiful. This book presents lectures delivered during the AMS Short Course entitled Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets, held at the Joint Mathematics Meetings in Cincinnati in January 1994. The lectures cover a wide range of topics, including the classical work of Julia and Fatou on local dynamics of analytic maps as well as recent work on the dynamics of quadratic and cubic polynomials, the geometry of Julia sets, and the structure of various parameter spaces. Among the other topics are recent results on Yoccoz puzzles and tableaux, limiting dynamics near parabolic points, the spider algorithm, extensions of the theory to rational maps, Newton's method, and entire transcendental functions. Much of the book is accessible to anyone with a background in the basics of dynamical systems and complex analysis.

Complex Dynamics

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Author : Robert L. Devaney
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Complex Dynamics written by Robert L. Devaney and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

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.

Quasiconformal Mappings In The Plane And Complex Dynamics

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Author : Luis T. Magalhães
language : en
Publisher: Springer Nature
Release Date : 2025-06-10

Quasiconformal Mappings In The Plane And Complex Dynamics written by Luis T. Magalhães and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-10 with Mathematics categories.

This book comprehensively explores the foundations of quasiconformal mappings in the complex plane, especially in view of applications to complex dynamics. Besides playing a crucial role in dynamical systems these mappings have important applications in complex analysis, geometry, topology, potential theory and partial differential equations, functional analysis and calculus of variations, electrostatics and nonlinear elasticity . The work covers standard material suitable for a one-year graduate-level course and extends to more advanced topics, in an accessible way even for students in an initial phase of university studies who have learned the basics of complex analysis at the usual level of a rigorous first one-semester course on the subject. At the frontier of complex analysis with real analysis, quasiconformal mappings appeared in 1859-60 in the cartography work of A. Tissot, well before the term “quasiconformal” was coined by L. Ahlfors in 1935. The detailed study of these mappings began in 1928 by H. Grötzsch, and L. Ahlfors’ seminal work published in 1935 significantly contributed to their development and was considered for awarding him the Fields Medal in 1936. The theory further evolved in 1937 and 1939 with O. Teichmüller’s contributions, and subsequent advancements are partially covered in this book. Organized into ten chapters with eight appendices, this work aims to provide an accessible, self-contained approach to the subject and includes examples at various levels and extensive applications to holomorphic dynamics. Throughout the text, historical notes contextualize advancements over time. A sequel to the author’s previous book, ‘Complex Analysis and Dynamics in One Variable with Applications,’ also published by Springer, this volume might be suitable for students in mathematics, physics, or engineering. A solid background in basic mathematical analysis is recommended to fully benefit from its content.

Handbook Of Dynamical Systems

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Author : B. Hasselblatt
language : en
Publisher: Elsevier
Release Date : 2002-08-20

Handbook Of Dynamical Systems written by B. Hasselblatt and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-20 with Mathematics categories.

Volumes 1A and 1B.These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample cross-references between individual surveys.The volumes are a valuable resource for dynamicists seeking to acquaint themselves with other specialties in the field, and to mathematicians active in other branches of mathematics who wish to learn about contemporary ideas and results dynamics. Assuming only general mathematical knowledge the surveys lead the reader towards the current state of research in dynamics.Volume 1B will appear 2005.

Complexity And Control Towards A Rigorous Behavioral Theory Of Complex Dynamical Systems

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Author : Vladimir G Ivancevic
language : en
Publisher: World Scientific
Release Date : 2014-11-07

Complexity And Control Towards A Rigorous Behavioral Theory Of Complex Dynamical Systems written by Vladimir G Ivancevic and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-07 with Science categories.

The book Complexity and Control: Towards a Rigorous Behavioral Theory of Complex Dynamical Systems is a graduate-level monographic textbook, intended to be a novel and rigorous contribution to modern Complexity Theory.This book contains 11 chapters and is designed as a one-semester course for engineers, applied and pure mathematicians, theoretical and experimental physicists, computer and economic scientists, theoretical chemists and biologists, as well as all mathematically educated scientists and students, both in industry and academia, interested in predicting and controlling complex dynamical systems of arbitrary nature.

Early Days In Complex Dynamics

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Author : Daniel S. Alexander
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

Early Days In Complex Dynamics written by Daniel S. Alexander and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

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.

Real And Complex Dynamical Systems

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Author : B. Branner
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Real And Complex Dynamical Systems written by B. Branner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

This volume contains edited versions of 11 contributions given by main speakers at the NATO Advanced Study Institute on lReal and Complex Dynamical Systems in Hiller0d, Denmark, June 20th - July 2nd, 1993. The vision of the institute was to illustrate the interplay between two important fields of Mathematics: Real Dynamical Systems and Complex Dynamical Systems. The interaction between these two fields has been growing over the years. Problems in Real Dynamical Systems have recently been solved using complex tools in the real or by extension to the complex. In return, problems in Complex Dynamical Systems have been settled using results from Real Dynamical Systems. The programme of the institute was to examine the state of the art of central parts of both Real and Complex Dynamical Systems, to reinforce contact between the two aspects of the theory and to make recent progress in each accessible to a larger group of mathematicians.

Recent Developments In Fractal Geometry And Dynamical Systems

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Author : Sangita Jha
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-18

Recent Developments In Fractal Geometry And Dynamical Systems written by Sangita Jha and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-18 with Mathematics categories.

This volume contains the proceedings of the virtual AMS Special Session on Fractal Geometry and Dynamical Systems, held from May 14–15, 2022. The content covers a wide range of topics. It includes nonautonomous dynamics of complex polynomials, theory and applications of polymorphisms, topological and geometric problems related to dynamical systems, and also covers fractal dimensions, including the Hausdorff dimension of fractal interpolation functions. Furthermore, the book contains a discussion of self-similar measures as well as the theory of IFS measures associated with Bratteli diagrams. This book is suitable for graduate students interested in fractal theory, researchers interested in fractal geometry and dynamical systems, and anyone interested in the application of fractals in science and engineering. This book also offers a valuable resource for researchers working on applications of fractals in different fields.