Chaotic and Fractal Dynamics

Introduction for Applied Scientists and Engineers

Author: Francis C. Moon

Publisher: John Wiley & Sons

ISBN: 3527617515

Category: Science

Page: 528

View: 8183

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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 and Fractals

Author: Michael F. Barnsley,Stephen G. Demko

Publisher: Academic Press

ISBN: 1483269086

Category: Mathematics

Page: 304

View: 9937

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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 and Fractals

The Mathematics Behind the Computer Graphics

Author: Robert L. Devaney,Linda Keen,Kathleen T. Alligood

Publisher: American Mathematical Soc.

ISBN: 0821801376

Category: Mathematics

Page: 148

View: 972

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This volume contains the proceedings of a highly successful AMS Short Course on Chaos and Fractals, held during the AMS Centennial Celebration in Providence, Rhode Island in August 1988. Chaos and fractals have been the subject of great interest in recent years and have proven to be useful in a variety of areas of mathematics and the sciences. The purpose of the short course was to provide a solid introduction to the mathematics underlying the notions of chaos and fractals. The papers in this book range over such topics as dynamical systems theory, Julia sets, the Mandelbrot set, attractors, the Smale horseshoe, calculus on fractals, and applications to data compression. The authors represented here are some of the top experts in this field. Aimed at beginning graduate students, college and university mathematics instructors, and non-mathematics researchers, this book provides readable expositions of several exciting topics of contemporary research.

Chaos, Dynamics, and Fractals

An Algorithmic Approach to Deterministic Chaos

Author: Joseph L. McCauley

Publisher: Cambridge University Press

ISBN: 9780521467476

Category: Mathematics

Page: 323

View: 3624

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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.

Chaos, Fractals, and Noise

Stochastic Aspects of Dynamics

Author: Andrzej Lasota,Michael C. Mackey

Publisher: Springer Science & Business Media

ISBN: 146124286X

Category: Mathematics

Page: 474

View: 9695

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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.

Chaos, Fractals, and Dynamics

Author: Fischer

Publisher: CRC Press

ISBN: 9780824773250

Category: Science

Page: 280

View: 7122

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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 Dynamics

An Introduction

Author: Gregory L. Baker,Jerry P. Gollub

Publisher: Cambridge University Press

ISBN: 9780521476850

Category: Mathematics

Page: 256

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New edition of a very successful undergraduate text on chaos.

Chaotic Dynamics

Fractals, Tilings, and Substitutions

Author: Geoffrey R. Goodson

Publisher: Cambridge University Press

ISBN: 1107112672

Category: Mathematics

Page: 350

View: 3444

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

Chaos and Fractals

New Frontiers of Science

Author: Heinz-Otto Peitgen,Hartmut Jürgens,Dietmar Saupe

Publisher: Springer Science & Business Media

ISBN: 1475747403

Category: Mathematics

Page: 999

View: 2542

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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.

Chaos in Dynamical Systems

Author: Edward Ott

Publisher: Cambridge University Press

ISBN: 9780521010849

Category: Mathematics

Page: 478

View: 1923

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New edition of the best-selling graduate textbook on chaos for scientists and engineers.

Fractals and Chaos in Geology and Geophysics

Author: Donald L. Turcotte

Publisher: Cambridge University Press

ISBN: 9780521567336

Category: Science

Page: 398

View: 5330

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Now in a greatly expanded second edition, this book relates fractals and chaos to a variety of geological and geophysical applications and introduces the fundamental concepts of fractal geometry and chaotic dynamics. In this new edition, Turcotte expands coverage of self-organized criticality and includes statistics and time series to provide a broad background for the reader. Topics include drainage networks and erosion, floods, earthquakes, mineral and petroleum resources, fragmentation, mantle convection, and magnetic field generation. The author introduces all concepts at the lowest possible level of mathematics consistent with their understanding, so that the reader requires only a background in basic physics and mathematics. He includes problems for the reader to solve. This book will appeal to a broad range of readers interested in complex natural phenomena.

Chaos and Fractals

An Elementary Introduction

Author: David P. Feldman

Publisher: Oxford University Press

ISBN: 0199566437

Category: Mathematics

Page: 408

View: 5087

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For students with a background in elementary algebra, this book provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia Sets and the Mandelbrot Set, power laws, and cellular automata. The book includes over 200 end-of-chapter exercises.

Chaos and Nonlinear Dynamics

An Introduction for Scientists and Engineers

Author: Robert C. Hilborn

Publisher: Oxford University Press on Demand

ISBN: 9780198507239

Category: Mathematics

Page: 650

View: 4477

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This is a comprehensive introduction to the exciting scientific field of nonlinear dynamics for students, scientists, and engineers, and requires only minimal prerequisites in physics and mathematics. The book treats all the important areas in the field and provides an extensive and up-to-date bibliography of applications in all fields of science, social science, economics, and even the arts.

Chaos and Fractals

A Computer Graphical Journey

Author: C.A. Pickover

Publisher: Elsevier

ISBN: 9780080528861

Category: Computers

Page: 452

View: 8357

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These days computer-generated fractal patterns are everywhere, from squiggly designs on computer art posters to illustrations in the most serious of physics journals. Interest continues to grow among scientists and, rather surprisingly, artists and designers. This book provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules. It also presents papers on seemingly paradoxical combinations of randomness and structure in systems of mathematical, physical, biological, electrical, chemical, and artistic interest. Topics include: iteration, cellular automata, bifurcation maps, fractals, dynamical systems, patterns of nature created through simple rules, and aesthetic graphics drawn from the universe of mathematics and art. Chaos and Fractals is divided into six parts: Geometry and Nature; Attractors; Cellular Automata, Gaskets, and Koch Curves; Mandelbrot, Julia and Other Complex Maps; Iterated Function Systems; and Computer Art. Additionally, information on the latest practical applications of fractals and on the use of fractals in commercial products such as the antennas and reaction vessels is presented. In short, fractals are increasingly finding application in practical products where computer graphics and simulations are integral to the design process. Each of the six sections has an introduction by the editor including the latest research, references, and updates in the field. This book is enhanced with numerous color illustrations, a comprehensive index, and the many computer program examples encourage reader involvement.

Fractal Physiology and Chaos in Medicine

Author: Bruce J West

Publisher: World Scientific

ISBN: 9814417815

Category: Mathematics

Page: 344

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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. Contents:IntroductionPhysiology in Fractal DimensionsDynamics in Fractal DimensionsStatistics in Fractal DimensionsApplications of Chaotic AttractorsPhysiologic Networks: The Final Chapter? Readership: Biomedical and physical scientists and students. Keywords:Fractals;Chaos;Physiology;Medicine;Nonlinear Dynamics;Networks;ComplexityReviews: “This book is an excellent introduction to nonlinear dynamics and fractals in medicine.” Zentralbatt MATH

Chaos, Noise and Fractals

Author: E. Roy Pike,L .A. Lugiato

Publisher: CRC Press

ISBN: 9780852743645

Category: Science

Page: 250

View: 5336

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The study of nonlinear dynamical systems has been gathering momentum since the late 1950s. It now constitutes one of the major research areas of modern theoretical physics. The twin themes of fractals and chaos, which are linked by attracting sets in chaotic systems that are fractal in structure, are currently generating a great deal of excitement. The degree of structure robustness in the presence of stochastic and quantum noise is thus a topic of interest. Chaos, Noise and Fractals discusses the role of fractals in quantum mechanics, the influence of phase noise in chaos and driven optical systems, and the arithmetic of chaos. The book represents a balanced overview of the field and is a worthy addition to the reading lists of researchers and students interested in any of the varied, and sometimes bizarre, aspects of this intriguing subject.

Fractals, Chaos, Power Laws

Minutes from an Infinite Paradise

Author: Manfred Schroeder

Publisher: Courier Corporation

ISBN: 0486472043

Category: Science

Page: 448

View: 7243

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This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author - hailed by Publishers Weekly as a modern Lewis Carroll - conveys memorable insights in the form of puns and puzzles. 1992 edition.