Complex Dynamics

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Complex Dynamics

Lennart Carleson,Theodore W. Gamelin
Complex Dynamics Book PDF

Author : Lennart Carleson,Theodore W. Gamelin
Publisher : Springer Science & Business Media
Page : 181 pages
File Size : 40,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781461243649

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Complex Dynamics by Lennart Carleson,Theodore W. Gamelin Pdf

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.

Complex Dynamics

Dierk Schleicher
Complex Dynamics Book PDF

Author : Dierk Schleicher
Publisher : CRC Press
Page : 663 pages
File Size : 40,6 Mb
Release : 2009-11-03
Category : Mathematics
ISBN : 9781439865422

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Complex Dynamics by Dierk Schleicher Pdf

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

A History of Complex Dynamics

Daniel S. Alexander
A History of Complex Dynamics Book PDF

Author : Daniel S. Alexander
Publisher : Springer Science & Business Media
Page : 175 pages
File Size : 43,6 Mb
Release : 2013-06-29
Category : Technology & Engineering
ISBN : 9783663091974

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A History of Complex Dynamics by Daniel S. Alexander Pdf

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.

Dynamics in One Complex Variable. (AM-160)

John Milnor
Dynamics in One Complex Variable AM 160 Book PDF

Author : John Milnor
Publisher : Princeton University Press
Page : 313 pages
File Size : 51,5 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 9781400835539

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Dynamics in One Complex Variable. (AM-160) by John Milnor Pdf

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.

Nonlinear and Complex Dynamics

José António Tenreiro Machado,Dumitru Baleanu,Albert C. J. Luo
Nonlinear and Complex Dynamics Book PDF

Author : José António Tenreiro Machado,Dumitru Baleanu,Albert C. J. Luo
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 51,7 Mb
Release : 2011-08-28
Category : Technology & Engineering
ISBN : 146140231X

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Nonlinear and Complex Dynamics by José António Tenreiro Machado,Dumitru Baleanu,Albert C. J. Luo Pdf

Nonlinear Dynamics of Complex Systems describes chaos, fractal and stochasticities within celestial mechanics, financial systems and biochemical systems. Part I discusses methods and applications in celestial systems and new results in such areas as low energy impact dynamics, low-thrust planar trajectories to the moon and earth-to-halo transfers in the sun, earth and moon. Part II presents the dynamics of complex systems including bio-systems, neural systems, chemical systems and hydro-dynamical systems. Finally, Part III covers economic and financial systems including market uncertainty, inflation, economic activity and foreign competition and the role of nonlinear dynamics in each.

Complex Dynamics and Renormalization (AM-135), Volume 135

Curtis T. McMullen
Complex Dynamics and Renormalization AM 135 Volume 135 Book PDF

Author : Curtis T. McMullen
Publisher : Princeton University Press
Page : 214 pages
File Size : 44,7 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882557

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Complex Dynamics and Renormalization (AM-135), Volume 135 by Curtis T. McMullen Pdf

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

Robert L. Devaney
Complex Dynamics Book PDF

Author : Robert L. Devaney
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 47,8 Mb
Release : 2006
Category : Domains of holomorphy
ISBN : 9780821836255

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Complex Dynamics by Robert L. Devaney Pdf

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.

Complex Dynamics and Morphogenesis

Chaouqi Misbah
Complex Dynamics and Morphogenesis Book PDF

Author : Chaouqi Misbah
Publisher : Springer
Page : 463 pages
File Size : 55,5 Mb
Release : 2016-12-01
Category : Science
ISBN : 9789402410204

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Complex Dynamics and Morphogenesis by Chaouqi Misbah Pdf

This book offers an introduction to the physics of nonlinear phenomena through two complementary approaches: bifurcation theory and catastrophe theory. Readers will be gradually introduced to the language and formalisms of nonlinear sciences, which constitute the framework to describe complex systems. The difficulty with complex systems is that their evolution cannot be fully predicted because of the interdependence and interactions between their different components. Starting with simple examples and working toward an increasing level of universalization, the work explores diverse scenarios of bifurcations and elementary catastrophes which characterize the qualitative behavior of nonlinear systems. The study of temporal evolution is undertaken using the equations that characterize stationary or oscillatory solutions, while spatial analysis introduces the fascinating problem of morphogenesis. Accessible to undergraduate university students in any discipline concerned with nonlinear phenomena (physics, mathematics, chemistry, geology, economy, etc.), this work provides a wealth of information for teachers and researchers in these various fields. Chaouqi Misbah is a senior researcher at the CNRS (National Centre of Scientific Research in France). His work spans from pattern formation in nonlinear science to complex fluids and biophysics. In 2002 he received a major award from the French Academy of Science for his achievements and in 2003 Grenoble University honoured him with a gold medal. Leader of a group of around 40 scientists, he is a member of the editorial board of the French Academy of Science since 2013 and also holds numerous national and international responsibilities.

C.G. JUNG'S COMPLEX DYNAMICS AND THE CLINICAL RELATIONSHIP

Brenda A. Donahue
C G JUNG S COMPLEX DYNAMICS AND THE CLINICAL RELATIONSHIP Book PDF

Author : Brenda A. Donahue
Publisher : Charles C Thomas Publisher
Page : 302 pages
File Size : 41,9 Mb
Release : 2003-01-01
Category : Complexes (Psychology)
ISBN : 9780398084226

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C.G. JUNG'S COMPLEX DYNAMICS AND THE CLINICAL RELATIONSHIP by Brenda A. Donahue Pdf

This book attempts to link Jung's theories of complex and archetype with processes involved in ego development, human relationship and attachment by using clinical examples. It is one way for therapists to understand Jung's ideas and use them in the clinical setting. The purpose of the book is to evoke questions rather than provide answers. When we ask what it is that transforms people in therapy, we must answer that we do not know. Healing is a mystery. This book provides multiple viewing points into mystery and highlights the undeniable fact that it appears within the clinical hour. The ideas presented in this book are intended to bridge the gap between "clinical" and "archetypal"by focusing on the clinical relationship. Techniques to activate the unconscious are presented in order to help the reader learn to develop a therapeutic space to contain the expression of what the client cannot yet verbalize and support the development of a mutual and shared language based upon the client's own material. The reader is encouraged to practice the individual experiential exercises presented in the last chapter to test the book's ideas and develop both questions and clinical skills based upon the theoretical material. Finally, the reader will be introduced to group experiential exercises that can be used with colleagues interested in working together to develop clinical skills. This book is useful for social workers, nurses, psychiatrists, psychologists, psychotherapists, counselors and human resource professionals.

Dynamics in Action

Alicia Juarrero
Dynamics in Action Book PDF

Author : Alicia Juarrero
Publisher : MIT Press
Page : 306 pages
File Size : 40,9 Mb
Release : 2002-01-25
Category : Psychology
ISBN : 0262600471

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Dynamics in Action by Alicia Juarrero Pdf

What is the difference between a wink and a blink? The answer is important not only to philosophers of mind, for significant moral and legal consequences rest on the distinction between voluntary and involuntary behavior. However, "action theory"—the branch of philosophy that has traditionally articulated the boundaries between action and non-action, and between voluntary and involuntary behavior—has been unable to account for the difference. Alicia Juarrero argues that a mistaken, 350-year-old model of cause and explanation—one that takes all causes to be of the push-pull, efficient cause sort, and all explanation to be prooflike—underlies contemporary theories of action. Juarrero then proposes a new framework for conceptualizing causes based on complex adaptive systems. Thinking of causes as dynamical constraints makes bottom-up and top-down causal relations, including those involving intentional causes, suddenly tractable. A different logic for explaining actions—as historical narrative, not inference—follows if one adopts this novel approach to long-standing questions of action and responsibility.

Rotation Sets and Complex Dynamics

Saeed Zakeri
Rotation Sets and Complex Dynamics Book PDF

Author : Saeed Zakeri
Publisher : Springer
Page : 124 pages
File Size : 52,9 Mb
Release : 2018-06-23
Category : Mathematics
ISBN : 9783319788104

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Rotation Sets and Complex Dynamics by Saeed Zakeri Pdf

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 Dynamical Systems in Education

Matthijs Koopmans,Dimitrios Stamovlasis
Complex Dynamical Systems in Education Book PDF

Author : Matthijs Koopmans,Dimitrios Stamovlasis
Publisher : Springer
Page : 412 pages
File Size : 41,8 Mb
Release : 2016-02-19
Category : Education
ISBN : 9783319275772

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Complex Dynamical Systems in Education by Matthijs Koopmans,Dimitrios Stamovlasis Pdf

This book capitalizes on the developments in dynamical systems and education by presenting some of the most recent advances in this area in seventeen non-overlapping chapters. The first half of the book discusses the conceptual framework of complex dynamical systems and its applicability to educational processes. The second half presents a set of empirical studies that that illustrate the use of various research methodologies to investigate complex dynamical processes in education, and help the reader appreciate what we learn about dynamical processes in education from using these approaches.

Transient Chaos

Ying-Cheng Lai,Tamás Tél
Transient Chaos Book PDF

Author : Ying-Cheng Lai,Tamás Tél
Publisher : Springer Science & Business Media
Page : 499 pages
File Size : 51,9 Mb
Release : 2011-02-26
Category : Mathematics
ISBN : 9781441969873

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Transient Chaos by Ying-Cheng Lai,Tamás Tél Pdf

The aim of this Book is to give an overview, based on the results of nearly three decades of intensive research, of transient chaos. One belief that motivates us to write this book is that, transient chaos may not have been appreciated even within the nonlinear-science community, let alone other scientific disciplines.

Thinking in Complexity

Klaus Mainzer
Thinking in Complexity Book PDF

Author : Klaus Mainzer
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 54,8 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783662030141

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Thinking in Complexity by Klaus Mainzer Pdf

Complexity and nonlinearity are prominent features in the evolution of matter, life, and human society. Even our mind seems to be governed by the nonlinear dynamics of the complex networks in our brain. This book considers complex systems in the physical and biological sciences, cognitive and computer sciences, social and economic sciences, and philosophy and history of science. An in terdisciplinary methodology is introduced to explain the emergence of order in nature and mind and in the econ omy and society by common principles. These methods are sometimes said to foreshadow the new sciences of complexity characterizing the scientific deve10pment of the 21 st century. The book critically an alyzes the successes and limits of this approach, its sys tematic foundations, and its historical and philosophical background. An epilogue discusses new standards of eth ical behavior which are demanded by the complex prob lems of nature and mind, economy and society.

Iteration of Rational Functions

Alan F. Beardon
Iteration of Rational Functions Book PDF

Author : Alan F. Beardon
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 46,8 Mb
Release : 2000-09-27
Category : Mathematics
ISBN : 0387951512

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Iteration of Rational Functions by Alan F. Beardon Pdf

This book focuses on complex analytic dynamics, which dates from 1916 and is currently attracting considerable interest. The text provides a comprehensive, well-organized treatment of the foundations of the theory of iteration of rational functions of a complex variable. The coverage extends from early memoirs of Fatou and Julia to important recent results and methods of Sullivan and Shishikura. Many details of the proofs have not appeared in print before.