Chaos and Fractals

An Elementary Introduction

Author: David P. Feldman

Publisher: Oxford University Press

ISBN: 0199566445

Category: Mathematics

Page: 408

View: 1594

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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.
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Fractals and Chaos

An illustrated course

Author: Paul S. Addison

Publisher: CRC Press

ISBN: 9780750304009

Category: Science

Page: 256

View: 5303

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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.
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Elementary Introduction to Spatial and Temporal Fractals

Author: L.T. Fan,D. Neogi,M. Yashima

Publisher: Springer Science & Business Media

ISBN: 3642456901

Category: Science

Page: 168

View: 3186

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Fractals play an important role in modeling natural phenomena and engineering processes. And fractals have a close connection to the concepts of chaotic dynamics. This monograph presents definitions, concepts, notions and methodologies of both spatial and temporal fractals. It addresses students and researchers in chemistry and in chemical engineering. The authors present the concepts and methodologies in sufficient detail for uninitiated readers. They include many simple examples and graphical illustrations. They outline some examples in more detail: Perimeter fractal dimension of char particles, surface fractal dimension of charcoal; fractal analysis of pressure fluctuation in multiphase flow systems. Readers who master the concepts in this book, can confidently apply them to their fields of interest.
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Chaotic Dynamics

Fractals, Tilings, and Substitutions

Author: Geoffrey R. Goodson

Publisher: Cambridge University Press

ISBN: 1107112672

Category: Mathematics

Page: 350

View: 6874

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

Dynamics, Fractals, and Rapid Fluctuations

Author: Goong Chen,Yu Huang

Publisher: Morgan & Claypool Publishers

ISBN: 159829914X

Category: Mathematics

Page: 227

View: 9472

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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
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Encounters with Chaos and Fractals, Second Edition

Author: Denny Gulick

Publisher: CRC Press

ISBN: 146655875X

Category: Mathematics

Page: 387

View: 4408

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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.
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Chaos and Fractals

New Frontiers of Science

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

Publisher: Springer Science & Business Media

ISBN: 0387202293

Category: Mathematics

Page: 864

View: 5968

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The fourteen chapters of this book cover the central ideas and concepts of chaos and fractals as well as many related topics including: the Mandelbrot set, Julia sets, cellular automata, L-systems, percolation and strange attractors. This new edition has been thoroughly revised throughout. The appendices of the original edition were taken out since more recent publications cover this material in more depth. Instead of the focussed computer programs in BASIC, the authors provide 10 interactive JAVA-applets for this second edition.
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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: 8439

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

Nonlinear Dynamics, Chaos and Fractals

Author: Willi-Hans Steeb

Publisher: World Scientific Publishing Company

ISBN: 9813109947

Category: Science

Page: 252

View: 5314

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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.
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Chaotic Dynamics

An Introduction Based on Classical Mechanics

Author: Tamás Tél,Márton Gruiz

Publisher: Cambridge University Press

ISBN: 9780521547833

Category: Mathematics

Page: 393

View: 6981

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A clear introduction to chaotic phenomena for undergraduate students in science, engineering, and mathematics.
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