Real And Complex Dynamical Systems

Author : B. Branner,Poul Hjorth
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 55,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401584395

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Real and Complex Dynamical Systems by B. Branner,Poul Hjorth Pdf

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.

Author : Mark Agranovsky,Anatoly Golberg,Fiana Jacobzon,David Shoikhet,Lawrence Zalcman
Publisher : Birkhäuser
Page : 372 pages
File Size : 47,7 Mb
Release : 2018-01-31
Category : Mathematics
ISBN : 9783319701547

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Complex Analysis and Dynamical Systems by Mark Agranovsky,Anatoly Golberg,Fiana Jacobzon,David Shoikhet,Lawrence Zalcman Pdf

This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences. Traditional methods and approaches surface in physics and in the life and engineering sciences with increasing frequency – the Schramm‐Loewner evolution, Laplacian growth, and quadratic differentials are just a few typical examples. This book provides a representative overview of these processes and collects open problems in the various areas, while at the same time showing where and how each particular topic evolves. This volume is dedicated to the memory of Alexander Vasiliev.

Author : Matthijs Koopmans,Dimitrios Stamovlasis
Publisher : Springer
Page : 412 pages
File Size : 44,8 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.

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
Page : 1885 pages
File Size : 46,6 Mb
Release : 2011-10-05
Category : Mathematics
ISBN : 9781461418054

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Mathematics of Complexity and Dynamical Systems by Robert A. Meyers Pdf

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Author : M. Reza Rahimi Tabar
Publisher : Springer
Page : 280 pages
File Size : 55,5 Mb
Release : 2019-07-04
Category : Science
ISBN : 9783030184728

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Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems by M. Reza Rahimi Tabar Pdf

This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation? Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data. The book provides an overview of methods that have been developed for the analysis of fluctuating time series and of spatially disordered structures. Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating time series and spatially disordered structures of complex systems studied in scientific fields such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and the neurosciences, and has led to a number of important results. The book also includes the numerical and analytical approaches to the analyses of complex time series that are most common in the physical and natural sciences. Further, it is self-contained and readily accessible to students, scientists, and researchers who are familiar with traditional methods of mathematics, such as ordinary, and partial differential equations. The codes for analysing continuous time series are available in an R package developed by the research group Turbulence, Wind energy and Stochastic (TWiSt) at the Carl von Ossietzky University of Oldenburg under the supervision of Prof. Dr. Joachim Peinke. This package makes it possible to extract the (stochastic) evolution equation underlying a set of data or measurements.

Author : Kevin M. Pilgrim
Publisher : Unknown
Page : 132 pages
File Size : 41,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662178931

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Combinations of Complex Dynamical Systems by Kevin M. Pilgrim Pdf

Author : Robert L. Devaney
Publisher : American Mathematical Soc.
Page : 232 pages
File Size : 41,8 Mb
Release : 1994-12-20
Category : Analytic mappings
ISBN : 0821867547

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Complex Dynamical Systems by Robert L. Devaney Pdf

In the last fifteen years, 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.

Author : Araceli Bonifant
Publisher : American Mathematical Soc.
Page : 610 pages
File Size : 45,7 Mb
Release : 2014-11-05
Category : Mathematics
ISBN : 9781470409371

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Collected Papers of John Milnor by Araceli Bonifant Pdf

This volume is the seventh in the series "Collected Papers of John Milnor." Together with the preceding Volume VI, it contains all of Milnor's papers in dynamics, through the year 2012. Most of the papers are in holomorphic dynamics; however, there are two in real dynamics and one on cellular automata. Two of the papers are published here for the first time. The papers in this volume provide important and fundamental material in real and complex dynamical systems. Many have become classics, and have inspired further research in the field. Some of the questions addressed here continue to be important in current research. In some cases, there have been minor corrections or clarifications, as well as references to more recent work which answers questions raised by the author. The volume also includes an index to facilitate searching the book for specific topics.

Author : John Willard Milnor
Publisher : American Mathematical Soc.
Page : 562 pages
File Size : 50,7 Mb
Release : 1994
Category : Algebra
ISBN : 9780821891391

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Collected Papers of John Milnor by John Willard Milnor Pdf

Author : Gary G. Fogal,Marjolijn H. Verspoor
Publisher : John Benjamins Publishing Company
Page : 324 pages
File Size : 43,7 Mb
Release : 2020-06-04
Category : Foreign Language Study
ISBN : 9789027261144

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Complex Dynamic Systems Theory and L2 Writing Development by Gary G. Fogal,Marjolijn H. Verspoor Pdf

This volume integrates complex dynamic systems theory (CDST) and L2 writing scholarship through a collection of in-depth studies and commentary across a range of writing constructs, learning contexts, and second and foreign languages. The text is arranged thematically across four topics: (i) perspectives on complexity, accuracy, and fluency, (ii) new constructs, approaches, and domains of L2-writing scholarship, (iii) methodological issues, and finally (iv) curricular perspectives. This work should appeal to graduate students and academics interested in expanded discussions on CDST, highlighting its utility for theorizing and researching language change, and to L2 writing scholars curious about how this fresh approach to researching L2 development can inform understandings of how L2 writing develops. As a CDST approach to language change has matured and taken a place among the dominant epistemologies in the field, students and researchers of L2 development alike will benefit from this volume.

Author : John Milnor
Publisher : Princeton University Press
Page : 313 pages
File Size : 41,8 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.

Author : David P. Feldman
Publisher : Princeton University Press
Page : 262 pages
File Size : 44,7 Mb
Release : 2019-08-06
Category : Mathematics
ISBN : 9780691161525

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Chaos and Dynamical Systems by David P. Feldman Pdf

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.

Author : Claudius Gros
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 53,5 Mb
Release : 2010-09-24
Category : Science
ISBN : 9783642047060

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Complex and Adaptive Dynamical Systems by Claudius Gros Pdf

Discover a wide range of findings in quantitative complex system science that help us make sense of our complex world. Written at an introductory level, the book provides an accessible entry into this fascinating and vitally important subject.

Author : Heinz-Otto Peitgen,Peter H. Richter
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 51,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642617171

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The Beauty of Fractals by Heinz-Otto Peitgen,Peter H. Richter Pdf

Now approaching its tenth year, this hugely successful book presents an unusual attempt to publicise the field of Complex Dynamics. The text was originally conceived as a supplemented catalogue to the exhibition "Frontiers of Chaos", seen in Europe and the United States, and describes the context and meaning of these fascinating images. A total of 184 illustrations - including 88 full-colour pictures of Julia sets - are suggestive of a coffee-table book. However, the invited contributions which round off the book lend the text the required formality. Benoit Mandelbrot gives a very personal account, in his idiosyncratic self-centred style, of his discovery of the fractals named after him and Adrien Douady explains the solved and unsolved problems relating to this amusingly complex set.

Author : Yaneer Bar-yam
Publisher : CRC Press
Page : 866 pages
File Size : 44,6 Mb
Release : 2019-03-04
Category : Mathematics
ISBN : 9780429717598

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Dynamics Of Complex Systems by Yaneer Bar-yam Pdf

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.