Chaotic and Fractal Dynamics

An Introduction for Applied Scientists and Engineers

Author: F. C. Moon

Publisher: John Wiley & Sons

ISBN: 9780471545712

Category: Science

Page: 508

View: 8217

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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 and Fractal Dynamics

Introduction for Applied Scientists and Engineers

Author: Francis C. Moon

Publisher: John Wiley & Sons

ISBN: 3527617515

Category: Science

Page: 528

View: 809

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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.

Problems and Solutions

Nonlinear Dynamics, Chaos and Fractals

Author: Willi-Hans Steeb

Publisher: World Scientific Publishing Company

ISBN: 9813109947

Category: Science

Page: 252

View: 6671

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This book presents a collection of problems for nonlinear dynamics, chaos theory and fractals. Besides the solved problems, supplementary problems are also added. Each chapter contains an introduction with suitable definitions and explanations to tackle the problems. The material is self-contained, and the topics range in difficulty from elementary to advanced. While students can learn important principles and strategies required for problem solving, lecturers will also find this text useful, either as a supplement or text, since concepts and techniques are developed in the problems.

Chaos, Fractals, and Dynamics

Author: Fischer

Publisher: CRC Press

ISBN: 9780824773250

Category: Science

Page: 280

View: 3406

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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 vibrations

an introduction for applied scientists and engineers

Author: F. C. Moon

Publisher: Wiley-Interscience

ISBN: 9780471856856

Category: Science

Page: 309

View: 3498

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Very Good,No Highlights or Markup,all pages are intact.

Problems and Solutions

Nonlinear Dynamics, Chaos and Fractals

Author: W.-H. Steeb

Publisher: World Scientific Publishing Company

ISBN: 9789813109926

Category: Chaotic behavior in systems

Page: 241

View: 7371

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One-dimensional maps -- Higher-dimensional maps and complex maps -- Fractals

Chaos, Fractals, and Dynamics

Computer Experiments in Mathematics

Author: Robert L. Devaney

Publisher: Addison Wesley Publishing Company

ISBN: 9780201232882

Category: Mathematics

Page: 181

View: 7910

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Introduces the mathematical topics of chaos, fractals, and dynamics using a combination of hands-on computer experimentation and precalculas mathmetics. A series of experiments produce fascinating computer graphics images of Julia sets, the Mandelbrot set, and fractals. The basic ideas of dynamics--chaos, iteration, and stability--are illustrated via computer projects.

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: 1240

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

Chaos and Nonlinear Dynamics

An Introduction for Scientists and Engineers

Author: Robert C. Hilborn,Amanda and Lisa Cross Professor of Physics Robert Hilborn

Publisher: Oxford University Press on Demand

ISBN: 9780198507239

Category: Mathematics

Page: 650

View: 5803

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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

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: 7440

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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.

Encounters with Chaos and Fractals, Second Edition

Author: Denny Gulick

Publisher: CRC Press

ISBN: 146655875X

Category: Mathematics

Page: 387

View: 3613

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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.

Applications of Chaos and Nonlinear Dynamics in Science and Engineering -

Author: Santo Banerjee,Lamberto Rondoni

Publisher: Springer

ISBN: 3642340172

Category: Science

Page: 296

View: 7768

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Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. This third volume concentrates on reviewing further relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. This encompasses, but is not limited to, topics such fluctuation relations and chaotic dynamics in physics, fractals and their applications in epileptic seizures, as well as chaos synchronization. Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘recipe book’ full of tried and tested, successful engineering applications.

Applied Dynamics

With Applications to Multibody and Mechatronic Systems

Author: Francis C. Moon

Publisher: John Wiley & Sons

ISBN: 9783527407514

Category: Technology & Engineering

Page: 581

View: 1697

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For almost a decade now, this textbook had been at the forefront in using modern analytical and computational codes and in addressing novel developments. Already used by numerous institutions for their courses, this second edition has been substantially revised, with new sections on biomechanics and micro- and nanotechnology. There is also more coverage of robotics, multibody simulations and celestial mechanics. Numerous examples have been added and problems, partly using MATLAB, have been included. * Free solutions manual available for lecturers at www.wiley-vch.de/supplements/

Chaotic Dynamics and Fractals

Author: Michael F. Barnsley,Stephen G. Demko

Publisher: Academic Press

ISBN: 1483269086

Category: Mathematics

Page: 304

View: 5823

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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.

Chaotic Maps

Dynamics, Fractals, and Rapid Fluctuations

Author: Goong Chen,Yu Huang

Publisher: Morgan & Claypool Publishers

ISBN: 159829914X

Category: Mathematics

Page: 227

View: 9006

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This book consists of lecture notes for a semester-long introductory graduate course on dynamical systems and chaos taught by the authors at Texas A&M University and Zhongshan University, China. There are ten chapters in the main body of the book, covering an elementary theory of chaotic maps in finite-dimensional spaces. The topics include one-dimensional dynamical systems (interval maps), bifurcations, general topological, symbolic dynamical systems, fractals and a class of infinite-dimensional dynamical systems which are induced by interval maps, plus rapid fluctuations of chaotic maps as a new viewpoint developed by the authors in recent years. Two appendices are also provided in order to ease the transitions for the readership from discrete-time dynamical systems to continuous-time dynamical systems, governed by ordinary and partial differential equations. Table of Contents: Simple Interval Maps and Their Iterations / Total Variations of Iterates of Maps / Ordering among Periods: The Sharkovski Theorem / Bifurcation Theorems for Maps / Homoclinicity. Lyapunoff Exponents / Symbolic Dynamics, Conjugacy and Shift Invariant Sets / The Smale Horseshoe / Fractals / Rapid Fluctuations of Chaotic Maps on RN / Infinite-dimensional Systems Induced by Continuous-Time Difference Equations

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: 5143

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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.

Chaotic Dynamics

Fractals, Tilings, and Substitutions

Author: Geoffrey R. Goodson

Publisher: Cambridge University Press

ISBN: 1107112672

Category: Mathematics

Page: 350

View: 1746

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

Vom Calculus zum Chaos

Author: David J. Acheson

Publisher: Walter de Gruyter

ISBN: 3486598996

Category: Mathematics

Page: 301

View: 3671

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Eine spannende Abhandlung zu ausgewählten Fragen der Mechanik quer durch die Jahrhunderte der Physik. Ohne großen mathematischen Ballast zeigt Acheson, wie hier die Infinitesimalrechnung - oder auch Calculus - den passenden Schlüssel zum Verständnis liefert. Das dynamische Verhalten der vorgestellten Systeme wird sowohl analytisch als auch mit Simulationen untersucht. Dazu werden QBasic-Programme verwendet, die so einfach sind, daß sie jeder leicht zum Laufen bringen und seinen Fragestellungen entsprechend anpassen kann. Der Inhalt wird durch historische Darstellungen der Mechanik und durch Bilder berühmter Physiker und Faksimiles ihrer Originaltexte bereichert. Das Buch für Studenten und Dozenten der Mathematik und Physik ist auch für interessierte Schüler der Oberstufe geeignet.