Chaotic Dynamics And Fractals

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Chaotic Dynamics and Fractals

Michael F. Barnsley,Stephen G. Demko
Chaotic Dynamics and Fractals Book PDF

Author : Michael F. Barnsley,Stephen G. Demko
Publisher : Academic Press
Page : 305 pages
File Size : 41,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483269085

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Chaotic Dynamics and Fractals by Michael F. Barnsley,Stephen G. Demko Pdf

Chaotic Dynamics and Fractals covers the proceedings of the 1985 Conference on Chaotic Dynamics, held at the Georgia Institute of Technology. This conference deals with the research area of chaos, dynamical systems, and fractal geometry. This text is organized into three parts encompassing 16 chapters. The first part describes the nature of chaos and fractals, the geometric tool for some strange attractors, and other complicated sets of data associated with chaotic systems. This part also considers the Henon-Hiles Hamiltonian with complex time, a Henon family of maps from C2 into itself, and the idea of turbulent maps in the course of presenting results on iteration of continuous maps from the unit interval to itself. The second part discusses complex analytic dynamics and associated fractal geometry, specifically the bursts into chaos, algorithms for obtaining geometrical and combinatorial information, and the parameter space for iterated cubic polynomials. This part also examines the differentiation of Julia sets with respects to a parameter in the associated rational map, permitting the formulation of Taylor series expansion for the sets. The third part highlights the applications of chaotic dynamics and fractals. This book will prove useful to mathematicians, physicists, and other scientists working in, or introducing themselves to, the field.

Chaos, Dynamics, and Fractals

Joseph L. McCauley
Chaos Dynamics and Fractals Book PDF

Author : Joseph L. McCauley
Publisher : Cambridge University Press
Page : 352 pages
File Size : 54,9 Mb
Release : 1994-05-26
Category : Science
ISBN : 9781107393271

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Chaos, Dynamics, and Fractals by Joseph L. McCauley Pdf

This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the emphasis makes it very different from all other books in the field. It provides the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects like universal critical exponents, devil's staircases and the Farey tree. The author uses a fully discrete method, a 'theoretical computer arithmetic', because finite (but not fixed) precision cannot be avoided in computation or experiment. This leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The connection is made with Turing's ideas of computable numbers and it is explained why the continuum approach leads to predictions that are not necessarily realized in computation or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed.

Encounters with Chaos and Fractals, Second Edition

Denny Gulick
Encounters with Chaos and Fractals Second Edition Book PDF

Author : Denny Gulick
Publisher : CRC Press
Page : 390 pages
File Size : 41,9 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9781584885177

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Encounters with Chaos and Fractals, Second Edition by Denny Gulick Pdf

Now with an extensive introduction to fractal geometry Revised and updated, Encounters with Chaos and Fractals, Second Edition provides an accessible introduction to chaotic dynamics and fractal geometry for readers with a calculus background. It incorporates important mathematical concepts associated with these areas and backs up the definitions and results with motivation, examples, and applications. Laying the groundwork for later chapters, the text begins with examples of mathematical behavior exhibited by chaotic systems, first in one dimension and then in two and three dimensions. Focusing on fractal geometry, the author goes on to introduce famous infinitely complicated fractals. He analyzes them and explains how to obtain computer renditions of them. The book concludes with the famous Julia sets and the Mandelbrot set. With more than enough material for a one-semester course, this book gives readers an appreciation of the beauty and diversity of applications of chaotic dynamics and fractal geometry. It shows how these subjects continue to grow within mathematics and in many other disciplines.

Chaos, Fractals, and Noise

Andrzej Lasota,Michael C. Mackey
Chaos Fractals and Noise Book PDF

Author : Andrzej Lasota,Michael C. Mackey
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 50,5 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461242864

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Chaos, Fractals, and Noise by Andrzej Lasota,Michael C. Mackey Pdf

The first edition of this book was originally published in 1985 under the ti tle "Probabilistic Properties of Deterministic Systems. " In the intervening years, interest in so-called "chaotic" systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma turing field. This interest in the serious usage of the concepts and techniques of nonlinear dynamics by applied scientists has probably been spurred more by the availability of inexpensive computers than by any other factor. Thus, computer experiments have been prominent, suggesting the wealth of phe nomena that may be resident in nonlinear systems. In particular, they allow one to observe the interdependence between the deterministic and probabilistic properties of these systems such as the existence of invariant measures and densities, statistical stability and periodicity, the influence of stochastic perturbations, the formation of attractors, and many others. The aim of the book, and especially of this second edition, is to present recent theoretical methods which allow one to study these effects. We have taken the opportunity in this second edition to not only correct the errors of the first edition, but also to add substantially new material in five sections and a new chapter.

Chaotic Dynamics

Geoffrey R. Goodson
Chaotic Dynamics Book PDF

Author : Geoffrey R. Goodson
Publisher : Cambridge University Press
Page : 419 pages
File Size : 41,8 Mb
Release : 2017
Category : Mathematics
ISBN : 9781107112674

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Chaotic Dynamics by Geoffrey R. Goodson Pdf

This rigorous undergraduate introduction to dynamical systems is an accessible guide for mathematics students advancing from calculus.

Chaos, Fractals, and Dynamics

Fischer
Chaos Fractals and Dynamics Book PDF

Author : Fischer
Publisher : CRC Press
Page : 282 pages
File Size : 44,9 Mb
Release : 1985-06-03
Category : Science
ISBN : 082477325X

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Chaos, Fractals, and Dynamics by Fischer Pdf

This timely work focuses on the recent expansion of research in the field of dynamical systems theory with related studies of chaos and fractals. Integrating the work of leading mathematicians, physicists, chemists, and engineers, this research-level monograph discusses different aspects of the concepts of chaos and fractals from both experimental and theoretical points of view. Featuring the most recent advances-including findings made possible by the development of digital computers-this authoritative work provides thorough understanding of known behavior of nonlinear dynamical systems as well as considerable insight into complex aspects not yet well understood. With a broad, multidisciplinary perspective and an ample supply of literature citations, Chaos, Fractals, and Dynamics is an invaluable reference and starting point for further research for scientists in all fields utilizing dynamical systems theory, including applied mathematicians, physicists, dynamists, chemists, biomathematicians, and graduate students in these areas. Book jacket.

Chaotic and Fractal Dynamics

Francis C. Moon
Chaotic and Fractal Dynamics Book PDF

Author : Francis C. Moon
Publisher : John Wiley & Sons
Page : 528 pages
File Size : 43,9 Mb
Release : 2008-11-20
Category : Science
ISBN : 9783527617517

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Chaotic and Fractal Dynamics by Francis C. Moon Pdf

A revision of a professional text on the phenomena of chaotic vibrations in fluids and solids. Major changes reflect the latest developments in this fast-moving topic, the introduction of problems to every chapter, additional mathematics and applications, more coverage of fractals, numerous computer and physical experiments. Contains eight pages of 4-color pictures.

Chaotic Dynamics

Gregory L. Baker,Jerry P. Gollub
Chaotic Dynamics Book PDF

Author : Gregory L. Baker,Jerry P. Gollub
Publisher : Cambridge University Press
Page : 282 pages
File Size : 45,5 Mb
Release : 1996
Category : Science
ISBN : 0521471060

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Chaotic Dynamics by Gregory L. Baker,Jerry P. Gollub Pdf

The previous edition of this text was the first to provide a quantitative introduction to chaos and nonlinear dynamics at the undergraduate level. It was widely praised for the clarity of writing and for the unique and effective way in which the authors presented the basic ideas. These same qualities characterize this revised and expanded second edition. Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had a far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. This second edition includes additional material on the analysis and characterization of chaotic data, and applications of chaos. This new edition of Chaotic Dynamics can be used as a text for courses on chaos for physics and engineering students at the second- and third-year level.

Fractals and Chaos

Paul S. Addison
Fractals and Chaos Book PDF

Author : Paul S. Addison
Publisher : CRC Press
Page : 276 pages
File Size : 45,9 Mb
Release : 1997-01-01
Category : Science
ISBN : 0849384435

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Fractals and Chaos by Paul S. Addison Pdf

Fractals and Chaos: An Illustrated Course provides you with a practical, elementary introduction to fractal geometry and chaotic dynamics-subjects that have attracted immense interest throughout the scientific and engineering disciplines. The book may be used in part or as a whole to form an introductory course in either or both subject areas. A prominent feature of the book is the use of many illustrations to convey the concepts required for comprehension of the subject. In addition, plenty of problems are provided to test understanding. Advanced mathematics is avoided in order to provide a concise treatment and speed the reader through the subject areas. The book can be used as a text for undergraduate courses or for self-study.

Dynamics with Chaos and Fractals

Marat Akhmet,Mehmet Onur Fen,Ejaily Milad Alejaily
Dynamics with Chaos and Fractals Book PDF

Author : Marat Akhmet,Mehmet Onur Fen,Ejaily Milad Alejaily
Publisher : Springer
Page : 0 pages
File Size : 45,5 Mb
Release : 2021-01-02
Category : Mathematics
ISBN : 3030358569

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Dynamics with Chaos and Fractals by Marat Akhmet,Mehmet Onur Fen,Ejaily Milad Alejaily Pdf

The book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. This is the first time in the literature that the description of chaos is initiated from a single motion. Chaos is now placed on the line of oscillations, and therefore, it is a subject of study in the framework of the theories of dynamical systems and differential equations, as in this book. The techniques introduced in the book make it possible to develop continuous and discrete dynamics which admit fractals as points of trajectories as well as orbits themselves. To provide strong arguments for the genericity of chaos in the real and abstract universe, the concept of abstract similarity is suggested.

Encounters with Chaos and Fractals

Denny Gulick
Encounters with Chaos and Fractals Book PDF

Author : Denny Gulick
Publisher : Unknown
Page : 371 pages
File Size : 54,9 Mb
Release : 2012
Category : Chaotic behavior in systems
ISBN : 0429097352

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Encounters with Chaos and Fractals by Denny Gulick Pdf

"PREFACE The far-reaching interest in chaos and fractals are outgrowths of the computer age. On the one hand, the notion of chaos is related to dynamics, or behavior, of physical systems. On the other hand, fractals are related to geometry, and appear as delightful but in nitely complex shapes on the line, in the plane or in space. Encounters with Chaos and Fractals is designed to give an introduction both to chaotic dynamics and to fractal geometry. During the past fty years the topics of chaotic dynamics and fractal geometry have become increasingly popular. Applications have extended to disciplines as diverse an electric circuits, weather prediction, orbits of satellites, chemical reactions, analysis of cloud formations and complicated coast lines, and the spread of disease. A fundamental reason for this popularity is the power of the computer, with its ability to produce complex calculations, and to create fascinating graphics. The computer has allowed scientists and mathematicians to solve problems in chaotic dynamics that hitherto seemed intractable, and to analyze scienti c data that in earlier times appeared to be either random or awed. Fractals, on the other hand, are basically geometric, but depend on many of the same mathematical properties that chaotic dynamics do. Mathematics lies at the foundation of chaotic dynamics and fractals. The very concepts that describe chaotic behavior and fractal graphs are mathematical in nature, whether they be analytic, geometric, algebraic or probabilistic. Some of these concepts are elementary, others are sophisticated. There are many books that discuss chaos and fractals in an expository manner, as there are treatises on chaos theory and fractal geometry written at the graduate level"--

Chaos and Fractals

Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe
Chaos and Fractals Book PDF

Author : Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe
Publisher : Springer Science & Business Media
Page : 1013 pages
File Size : 42,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475747409

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Chaos and Fractals by Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe Pdf

For almost ten years chaos and fractals have been enveloping many areas of mathematics and the natural sciences in their power, creativity and expanse. Reaching far beyond the traditional bounds of mathematics and science to the realms of popular culture, they have captured the attention and enthusiasm of a worldwide audience. The fourteen chapters of the book cover the central ideas and concepts, as well as many related topics including, the Mandelbrot Set, Julia Sets, Cellular Automata, L-Systems, Percolation and Strange Attractors, and each closes with the computer code for a central experiment. In the two appendices, Yuval Fisher discusses the details and ideas of fractal image compression, while Carl J.G. Evertsz and Benoit Mandelbrot introduce the foundations and implications of multifractals.

Chaotic Vibrations

Francis C. Moon
Chaotic Vibrations Book PDF

Author : Francis C. Moon
Publisher : Wiley-VCH
Page : 0 pages
File Size : 47,7 Mb
Release : 2004-06-07
Category : Science
ISBN : 0471679089

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Chaotic Vibrations by Francis C. Moon Pdf

Translates new mathematical ideas in nonlinear dynamics and chaos into a language that engineers and scientists can understand, and gives specific examples and applications of chaotic dynamics in the physical world. Also describes how to perform both computer and physical experiments in chaotic dynamics. Topics cover Poincare maps, fractal dimensions and Lyapunov exponents, illustrating their use in specific physical examples. Includes an extensive guide to the literature, especially that relating to more mathematically oriented works; a glossary of chaotic dynamics terms; a list of computer experiments; and details for a demonstration experiment on chaotic vibrations.

Chaos, Fractals, and Dynamics

P. Fischer
Chaos Fractals and Dynamics Book PDF

Author : P. Fischer
Publisher : CRC Press
Page : 282 pages
File Size : 52,6 Mb
Release : 2020-11-26
Category : Mathematics
ISBN : 9781000154221

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Chaos, Fractals, and Dynamics by P. Fischer Pdf

This book contains eighteen papers, all more-or-less linked to the theory of dynamical systems together with related studies of chaos and fractals. It shows many fractal configurations that were generated by computer calculations of underlying two-dimensional maps.

Fractal Physiology and Chaos in Medicine

Bruce J. West
Fractal Physiology and Chaos in Medicine Book PDF

Author : Bruce J. West
Publisher : World Scientific
Page : 345 pages
File Size : 50,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814417792

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Fractal Physiology and Chaos in Medicine by Bruce J. West Pdf

This exceptional book is concerned with the application of fractals and chaos, as well as other concepts from nonlinear dynamics to biomedical phenomena. Herein we seek to communicate the excitement being experienced by scientists upon making application of these concepts within the life sciences. Mathematical concepts are introduced using biomedical data sets and the phenomena being explained take precedence over the mathematics. In this new edition what has withstood the test of time has been updated and modernized; speculations that were not borne out have been expunged and the breakthroughs that have occurred in the intervening years are emphasized. The book provides a comprehensive overview of a nascent theory of medicine, including a new chapter on the theory of complex networks as they pertain to medicine.