Robert L. Devaney's Books

An Introduction To Chaotic Dynamical Systems

By: Robert L. Devaney

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An Introduction To Chaotic Dynamical Systems

By: Robert L. Devaney

There is an explosion of interest in dynamical systems in the mathematical community as well as in many areas of science. The results have been truly exciting: systems which once seemed completely intractable from an analytic point of view can now be understood in a geometric or qualitative sense rather easily. Scientists and engineers realize the power and the beauty of the geometric and qualitative techniques. These techniques apply to a number of important nonlinear problems ranging from physics and chemistry to ecology and economics. Computer graphics have allowed us to view the dynamical behavior geometrically. The appearance of incredibly beautiful and intricate objects such as the Mandelbrot set, the Julia set, and other fractals have really piqued interest in the field. This is text is aimed primarily at advanced undergraduate and beginning graduate students. Throughout, the author emphasizes the mathematical aspects of the theory of discrete dynamical systems, not the many and diverse applications of this theory. The field of dynamical systems and especially the study of chaotic systems has been hailed as one of the important breakthroughs in science in the past century and its importance continues to expand. There is no question that the field is becoming more and more important in a variety of scientific disciplines. New to this edition: •Greatly expanded coverage complex dynamics now in Chapter 2 •The third chapter is now devoted to higher dimensional dynamical systems. •Chapters 2 and 3 are independent of one another. •New exercises have been added throughout.

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434

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CRC Press

Published Date

ISBN 10

1000486761

ISBN 13

9781000486766

Differential Equations, Dynamical Systems, and an Introduction to Chaos

By: Morris W. Hirsch,Stephen Smale,Robert L. Devaney

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Differential Equations, Dynamical Systems, and an Introduction to Chaos

By: Morris W. Hirsch,Stephen Smale,Robert L. Devaney

Differential Equations, Dynamical Systems, and an Introduction to Chaos, now in its third edition, covers the dynamical aspects of ordinary differential equations. It explores the relations between dynamical systems and certain fields outside pure mathematics, and continues to be the standard textbook for advanced undergraduate and graduate courses in this area.""Written for students with a background in calculus and elementary linear algebra, the text is rigorous yet accessible and contains examples and explorations to reinforce learning." - BACK COVER.

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433

Publisher

Academic Press

Published Date

ISBN 10

0123820103

ISBN 13

9780123820105

Complex Dynamics

Twenty-five Years After the Appearance of the Mandelbrot Set : Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Complex Dynamics--Twenty-five Years After the Appearance of the Mandelbrot Set, June 13-17, 2004, Snowbird, Utah

By: Robert L. Devaney

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Complex Dynamics

By: Robert L. Devaney

Chaotic behavior of (even the simplest) iterations of polynomial maps of the complex plane was known for almost one hundred years due to the pioneering work of Farou, Julia, and their contemporaries. However, it was only twenty-five years ago that the first computer generated images illustrating properties of iterations of quadratic maps appeared. These images of the so-called Mandelbrot and Julia sets immediately resulted in a strong resurgence of interest in complex dynamics. The present volume, based on the talks at the conference commemorating the twenty-fifth anniversary of the appearance of Mandelbrot sets, provides a panorama of current research in this truly fascinating area of mathematics.

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218

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821836250

ISBN 13

9780821836255

Complex Dynamical Systems

The Mathematics Behind the Mandelbrot and Julia Sets

By: Robert L. Devaney

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Complex Dynamical Systems

The Mathematics Behind the Mandelbrot and Julia Sets

By: Robert L. Devaney

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.

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232

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821867547

ISBN 13

9780821867549

Chaos and Fractals: The Mathematics Behind the Computer Graphics

The Mathematics Behind the Computer Graphics

By: Robert L. Devaney,Kathleen T. Alligood

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Chaos and Fractals: The Mathematics Behind the Computer Graphics

The Mathematics Behind the Computer Graphics

By: Robert L. Devaney,Kathleen T. Alligood

The terms chaos and fractals have received widespread attention in recent years. The alluring computer graphics images associated with these terms have heightened interest among scientists in these ideas. This volume contains the introductory survey lectures delivered in the American Mathematical Society Short Course, Chaos and Fractals: The Mathematics Behind the Computer Graphics, on August 6-7, 1988, given in conjunction with the AMS Centennial Meeting in Providence, Rhode Island. In his overview, Robert L. Devaney introduces such key topics as hyperbolicity, the period doubling route to chaos, chaotic dynamics, symbolic dynamics and the horseshoe, and the appearance of fractals as the chaotic set for a dynamical system. Linda Keen and Bodil Branner discuss the Mandelbrot set and Julia sets associated to the complex quadratic family z -> z2 + c. Kathleen T. Alligood, James A. Yorke, and Philip J. Holmes discuss some of these topics in higher dimensional settings, including the Smale horseshoe and strange attractors. Jenny Harrison and Michael F. Barnsley give an overview of fractal geometry and its applications. -- from dust jacket.

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176

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American Mathematical Soc.

Published Date

ISBN 10

0821801376

ISBN 13

9780821801376

A First Course In Chaotic Dynamical Systems

Theory And Experiment

By: Robert L. Devaney

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A First Course In Chaotic Dynamical Systems

Theory And Experiment

By: Robert L. Devaney

A First Course in Chaotic Dynamical Systems: Theory and Experiment is the first book to introduce modern topics in dynamical systems at the undergraduate level. Accessible to readers with only a background in calculus, the book integrates both theory and computer experiments into its coverage of contemporary ideas in dynamics. It is designed as a gradual introduction to the basic mathematical ideas behind such topics as chaos, fractals, Newton's method, symbolic dynamics, the Julia set, and the Mandelbrot set, and includes biographies of some of the leading researchers in the field of dynamical systems. Mathematical and computer experiments are integrated throughout the text to help illustrate the meaning of the theorems presented. Chaotic Dynamical Systems Software, Labs 1-6 is a supplementary labouratory software package, available separately, that allows a more intuitive understanding of the mathematics behind dynamical systems theory. Combined with A First Course in Chaotic Dynamical Systems , it leads to a rich understanding of this emerging field.

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Page Count

339

Publisher

CRC Press

Published Date

ISBN 10

0429972032

ISBN 13

9780429972034

Differential Equations, Dynamical Systems, and Linear Algebra

By: Morris W. Hirsch,Robert L. Devaney,Stephen Smale

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Differential Equations, Dynamical Systems, and Linear Algebra

By: Morris W. Hirsch,Robert L. Devaney,Stephen Smale

This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.

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373

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Academic Press

Published Date

ISBN 10

0080873766

ISBN 13

9780080873763

An Introduction To Chaotic Dynamical Systems

By: Robert L. Devaney

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An Introduction To Chaotic Dynamical Systems

By: Robert L. Devaney

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434

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CRC Press

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ISBN 10

1000486761

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9781000486766

A First Course In Chaotic Dynamical Systems

Theory And Experiment

By: Robert L. L. Devaney

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A First Course In Chaotic Dynamical Systems

Theory And Experiment

By: Robert L. L. Devaney

A First Course in Chaotic Dynamical Systems: Theory and Experiment, Second Edition The long-anticipated revision of this well-liked textbook offers many new additions. In the twenty-five years since the original version of this book was published, much has happened in dynamical systems. Mandelbrot and Julia sets were barely ten years old when the first edition appeared, and most of the research involving these objects then centered around iterations of quadratic functions. This research has expanded to include all sorts of different types of functions, including higher-degree polynomials, rational maps, exponential and trigonometric functions, and many others. Several new sections in this edition are devoted to these topics. The area of dynamical systems covered in A First Course in Chaotic Dynamical Systems: Theory and Experiment, Second Edition is quite accessible to students and also offers a wide variety of interesting open questions for students at the undergraduate level to pursue. The only prerequisite for students is a one-year calculus course (no differential equations required); students will easily be exposed to many interesting areas of current research. This course can also serve as a bridge between the low-level, often non-rigorous calculus courses, and the more demanding higher-level mathematics courses. Features More extensive coverage of fractals, including objects like the Sierpinski carpet and others that appear as Julia sets in the later sections on complex dynamics, as well as an actual chaos "game." More detailed coverage of complex dynamical systems like the quadratic family and the exponential maps. New sections on other complex dynamical systems like rational maps. A number of new and expanded computer experiments for students to perform. About the Author Robert L. Devaney is currently professor of mathematics at Boston University. He received his PhD from the University of California at Berkeley under the direction of Stephen Smale. He taught at Northwestern University and Tufts University before coming to Boston University in 1980. His main area of research is dynamical systems, primarily complex analytic dynamics, but also including more general ideas about chaotic dynamical systems. Lately, he has become intrigued with the incredibly rich topological aspects of dynamics, including such things as indecomposable continua, Sierpinski curves, and Cantor bouquets.

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318

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CRC Press

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ISBN 10

1000065650

ISBN 13

9781000065657

An Introduction To Chaotic Dynamical Systems

By: Robert Devaney

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An Introduction To Chaotic Dynamical Systems

By: Robert Devaney

The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.

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280

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CRC Press

Published Date

ISBN 10

0429981937

ISBN 13

9780429981937

Differential Equations, Dynamical Systems, and an Introduction to Chaos

By: Morris W. Hirsch,Stephen Smale,Robert L. Devaney

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Differential Equations, Dynamical Systems, and an Introduction to Chaos

By: Morris W. Hirsch,Stephen Smale,Robert L. Devaney

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433

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Academic Press

Published Date

ISBN 10

0123820103

ISBN 13

9780123820105

Differential Equations, Dynamical Systems, and Linear Algebra

By: Morris W. Hirsch,Robert L. Devaney,Stephen Smale

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Differential Equations, Dynamical Systems, and Linear Algebra

By: Morris W. Hirsch,Robert L. Devaney,Stephen Smale

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373

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Academic Press

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ISBN 10

0080873766

ISBN 13

9780080873763

Chaos and Fractals: The Mathematics Behind the Computer Graphics

The Mathematics Behind the Computer Graphics

By: Robert L. Devaney,Kathleen T. Alligood

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Chaos and Fractals: The Mathematics Behind the Computer Graphics

The Mathematics Behind the Computer Graphics

By: Robert L. Devaney,Kathleen T. Alligood

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176

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American Mathematical Soc.

Published Date

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0821801376

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9780821801376

Book's by Robert L. Devaney

An Introduction To Chaotic Dynamical Systems

An Introduction To Chaotic Dynamical Systems

Differential Equations, Dynamical Systems, and an Introduction to Chaos

Differential Equations, Dynamical Systems, and an Introduction to Chaos

Complex Dynamics

Complex Dynamics

Complex Dynamical Systems

Complex Dynamical Systems

Chaos and Fractals: The Mathematics Behind the Computer Graphics

Chaos and Fractals: The Mathematics Behind the Computer Graphics

A First Course In Chaotic Dynamical Systems

A First Course In Chaotic Dynamical Systems

Differential Equations, Dynamical Systems, and Linear Algebra

Differential Equations, Dynamical Systems, and Linear Algebra

An Introduction To Chaotic Dynamical Systems

An Introduction To Chaotic Dynamical Systems

A First Course In Chaotic Dynamical Systems

A First Course In Chaotic Dynamical Systems

An Introduction To Chaotic Dynamical Systems

An Introduction To Chaotic Dynamical Systems

Differential Equations, Dynamical Systems, and an Introduction to Chaos

Differential Equations, Dynamical Systems, and an Introduction to Chaos

Differential Equations, Dynamical Systems, and Linear Algebra

Differential Equations, Dynamical Systems, and Linear Algebra

Chaos and Fractals: The Mathematics Behind the Computer Graphics

Chaos and Fractals: The Mathematics Behind the Computer Graphics

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