Download or read book A History of Complex Dynamics written by Daniel S. Alexander and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 175 pages. 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.
Download or read book Complex Dynamics written by Dierk Schleicher and published by CRC Press. This book was released on 2009-11-03 with total page 663 pages. 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
Download or read book Dynamics in One Complex Variable written by John Milnor and published by Princeton University Press. This book was released on 2011-02-11 with total page 313 pages. 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.
Download or read book Frontiers in Complex Dynamics written by Araceli Bonifant and published by Princeton University Press. This book was released on 2014-03-16 with total page 799 pages. 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.
Download or read book Nonlinear and Complex Dynamics written by José António Tenreiro Machado and published by Springer Science & Business Media. This book was released on 2011-08-28 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Historical Dynamics written by Peter Turchin and published by Princeton University Press. This book was released on 2018-05-08 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many historical processes are dynamic. Populations grow and decline. Empires expand and collapse. Religions spread and wither. Natural scientists have made great strides in understanding dynamical processes in the physical and biological worlds using a synthetic approach that combines mathematical modeling with statistical analyses. Taking up the problem of territorial dynamics--why some polities at certain times expand and at other times contract--this book shows that a similar research program can advance our understanding of dynamical processes in history. Peter Turchin develops hypotheses from a wide range of social, political, economic, and demographic factors: geopolitics, factors affecting collective solidarity, dynamics of ethnic assimilation/religious conversion, and the interaction between population dynamics and sociopolitical stability. He then translates these into a spectrum of mathematical models, investigates the dynamics predicted by the models, and contrasts model predictions with empirical patterns. Turchin's highly instructive empirical tests demonstrate that certain models predict empirical patterns with a very high degree of accuracy. For instance, one model accounts for the recurrent waves of state breakdown in medieval and early modern Europe. And historical data confirm that ethno-nationalist solidarity produces an aggressively expansive state under certain conditions (such as in locations where imperial frontiers coincide with religious divides). The strength of Turchin's results suggests that the synthetic approach he advocates can significantly improve our understanding of historical dynamics.
Download or read book Chaos and Order written by N. Katherine Hayles and published by University of Chicago Press. This book was released on 2014-12-10 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: The scientific discovery that chaotic systems embody deep structures of order is one of such wide-ranging implications that it has attracted attention across a spectrum of disciplines, including the humanities. In this volume, fourteen theorists explore the significance for literary and cultural studies of the new paradigm of chaotics, forging connections between contemporary literature and the science of chaos. They examine how changing ideas of order and disorder enable new readings of scientific and literary texts, from Newton's Principia to Ruskin's autobiography, from Victorian serial fiction to Borges's short stories. N. Katherine Hayles traces shifts in meaning that chaos has undergone within the Western tradition, suggesting that the science of chaos articulates categories that cannot be assimilated into the traditional dichotomy of order and disorder. She and her contributors take the relation between order and disorder as a theme and develop its implications for understanding texts, metaphors, metafiction, audience response, and the process of interpretation itself. Their innovative and diverse work opens the interdisciplinary field of chaotics to literary inquiry.
Download or read book Thinking in Complexity written by Klaus Mainzer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first edition sold out in less than a year, we now present the revised second edition of Mainzer's popular book. The theory of nonlinear complex systems has become a successful problem-solving approach in the natural sciences from laser physics, quantum chaos, and meteorology to computer simulations of cell growth in biology. It is now recognized that many of our social, ecological, and political problems are also of a global, complex, and nonlinear nature. And one of the most exciting contemporary topics is the idea that even the human mind is governed largely by the nonlinear dynamics of complex systems. In this wide-ranging but concise treatment, Prof. Mainzer discusses, in a nontechnical language, the common framework behind these endeavors. Emphasis is given to the evolution of new structures in natural and cultural systems and we see clearly how the new integrative approach can give insights not available from traditional reductionistic methods.
Download or read book Complex Economic Dynamics written by Richard H. Day and published by . This book was released on 2000-02 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: V. 1. An introduction to dynamical systems and market mechanisms -- v. 2. An introduction to macroeconomics dynamics.
Download or read book Dynamics Of Complex Systems written by Yaneer Bar-yam and published by CRC Press. This book was released on 2019-03-04 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Dynamics in Action written by Alicia Juarrero and published by MIT Press. This book was released on 2002-01-25 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Holomorphic Dynamics written by S. Morosawa and published by Cambridge University Press. This book was released on 2000-01-13 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2000, is a comprehensive introduction to holomorphic dynamics, that is the dynamics induced by the iteration of various analytic maps in complex number spaces. This has been the focus of much attention in recent years, with, for example, the discovery of the Mandelbrot set, and work on chaotic behaviour of quadratic maps. The treatment is mathematically unified, emphasizing the substantial role played by classical complex analysis in understanding holomorphic dynamics as well as giving an up-to-date coverage of the modern theory. The authors cover entire functions, Kleinian groups and polynomial automorphisms of several complex variables such as complex Henon maps, as well as the case of rational functions. The book will be welcomed by graduate students and professionals in pure mathematics and science who seek a reasonably self-contained introduction to this exciting area.
Download or read book Early Days in Complex Dynamics written by Daniel S. Alexander and published by American Mathematical Soc.. This book was released on 2012 with total page 474 pages. 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.
Download or read book Chaos and Dynamical Systems written by David P. Feldman and published by Princeton University Press. This book was released on 2019-08-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview. In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder. Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.
Download or read book Complex Population Dynamics written by Peter Turchin and published by Princeton University Press. This book was released on 2003-02-02 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why do organisms become extremely abundant one year and then seem to disappear a few years later? Why do population outbreaks in particular species happen more or less regularly in certain locations, but only irregularly (or never at all) in other locations? Complex population dynamics have fascinated biologists for decades. By bringing together mathematical models, statistical analyses, and field experiments, this book offers a comprehensive new synthesis of the theory of population oscillations. Peter Turchin first reviews the conceptual tools that ecologists use to investigate population oscillations, introducing population modeling and the statistical analysis of time series data. He then provides an in-depth discussion of several case studies--including the larch budmoth, southern pine beetle, red grouse, voles and lemmings, snowshoe hare, and ungulates--to develop a new analysis of the mechanisms that drive population oscillations in nature. Through such work, the author argues, ecologists can develop general laws of population dynamics that will help turn ecology into a truly quantitative and predictive science. Complex Population Dynamics integrates theoretical and empirical studies into a major new synthesis of current knowledge about population dynamics. It is also a pioneering work that sets the course for ecology's future as a predictive science.
Download or read book Lyapunov Exponents written by Arkady Pikovsky and published by Cambridge University Press. This book was released on 2016-02-11 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Utilising a pragmatic, physical approach, this self-contained book provides a comprehensive description of the concept. Beginning with the basic properties and numerical methods, it then guides readers through to the most recent advances in applications to complex systems. Practical algorithms are thoroughly reviewed and their performance is discussed, while a broad set of examples illustrate the wide range of potential applications. The description of various numerical and analytical techniques for the computation of Lyapunov exponents offers an extensive array of tools for the characterization of phenomena such as synchronization, weak and global chaos in low and high-dimensional set-ups, and localization. This text equips readers with all the investigative expertise needed to fully explore the dynamical properties of complex systems, making it ideal for both graduate students and experienced researchers.
Download or read book An Introduction To Chaotic Dynamical Systems written by Robert Devaney and published by CRC Press. This book was released on 2018-03-09 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.
