Books by Robert L. Devaney


A FIRST COURSE IN CHAOTIC DYNAMICAL SYSTEMS, Second Edition

Now published by CRC Press, Taylor and Francis Group, 2020, ISBN 978-0-367-23599-4.

This is an undergraduate textbook about chaotic dynamical systems. The only prerequisites are a background in calculus and an interest in mathematics. Topics covered include iteration, bifurcations, symbolic dynamics, Sharkovsky's theorem, chaos, the Schwarzian derivative, Newton's method, fractals, Julia sets, and the Mandelbrot set. Numerous computer experiments are also included. Japanese translation (2001).

DIFFERENTIAL EQUATIONS, DYNAMICAL SYSTEMS, AND AN INTRODUCTION TO CHAOS, Third Edition.

 Elsevier Academic Press. ISBN 978-0-12-382010-5 (2013).

Japanese edition Kyoritsu Shuppan Co., Ltd. (2017).

With M. W. Hirsch and S. Smale. This is a text for an advanced undergraduate or graduate course in Differential Equations. It is a completely revised and updated version of the classic Hirsch-Smale text called Differential Equations, Dynamical Systems and Linear Algebra. Japanese translation (2004). Chinese translation (2008).
Text home page and list of errata.

AN INTRODUCTION TO CHAOTIC DYNAMICAL SYSTEMS.

Third Edition. Now published by CRC Press, 2022, ISBN 978-1032150468.

This book is intended for graduate students and advanced undergraduates in mathematics as well as researchers in other fields who wish to understand more about dynamical systems theory. Half of the book is devoted to one-dimensional dynamics, while the remainder is equally split between higher dimensional dynamics and complex dynamics. The newest edition contains a much more detailed exposition of topics in complex dynamics such as the Mandelbrot and Julia sets, as well as the different types of dynamics that occur for maps such as exponential and rational maps. Japanese translation of the second edition (2004).

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DIFFERENTIAL EQUATIONS

Differential Equations, Fourth Edition. By Blanchard, Devaney, Hall. Published by Brooks/Cole, Cengage Learning, 2011. ISBN 13: 978-0-495-56198-9.

Spanish Edition: Ecuaciones Diferenciales. Blanchard, Devaney, Hall. International Thomson Editores, 1999.
ISBN: 968-7529-63-6

This book is a sophomore level ordinary differential equations book written from a dynamical systems point of view. Funded by the National Science Foundation (The BU Differential Equations Project), the book is an attempt to infuse modern topics in differential equations into the lower level course. Emphasis in the book is on the qualitative aspects of the theory rather than analytic solutions. The first edition of this book was published by Brooks-Cole in 1998. For more information, send e-mail to odes@math.bu.edu.

MASTERING DIFFERENTIAL EQUATIONS: THE VISUAL METHOD

 The Teaching Company. ISBN 1-59803-743-9 (2004). This is a guidebook that accompanies a series of twenty four 30 minute videos that give an introduction to differential equations. Also available at The Great Courses coupon page.

A TOOLKIT OF DYNAMICS ACTIVITIES

This is a series of four paperback books on dynamical systems for high school students and their teachers. The books progress in level from grades 7-9 (Iteration and Fractals), grades 10-11 (Chaos), and grade 12 (The Mandelbrot and Julia Sets).


Iteration: A Toolkit of Dynamics Activites. Key Curriculum Press, 1998. With J. Choate and A. Foster.

Fractals: A Toolkit of Dynamics Activities. Key Curriculum Press, 1998. With J. Choate and A. Foster.

Chaos: A Toolkit of Dynamics Activities. Key Curriculum Press, 1999. With J. Choate.

The Mandelbrot and Julia sets: A Toolkit of Dynamics Activities. Key Curriculum Press, 1999.

CHAOS, FRACTALS, AND DYNAMICS: COMPUTER EXPERIMENTS IN MATHEMATICS.

Now published by Pearson Learning. www.pearsonlearning.com ISBN 0-201-23288-X. Telephone: 800-526-9907

This text is aimed at high school students and their teachers. It aims to explain some of the recent discoveries in mathematics using a combination of high school algebra and computer experiments. Simple BASIC programs are included for all major topics in the book. Topics include iteration, chaos, fractals, the Mandelbrot and Julia sets. Italian translation (1990). Dutch translation (1992).

CONFORMAL DYNAMICS AND HYPERBOLIC GEOMETRY

American Mathematical Society, ISBN 0-8218-3625-0. Contemporary Mathematics, 573, 2012. Coedited with F. Bonahon, F. P. Gardiner, and D. Saric. This is the Proceedings of a conference on Complex Dynamics and Hyperbolic Geometry held at the Graduate Center, CUNY, October 21-23, 2010 in honor of Linda Keen's 70th birthday.

FRACTALS, WAVELETS, AND THEIR APPLICATIONS

Springer-Verlag, ISBN 978-3-319-08105-2, 2014. Coedited with C. Bandt, M. Barnsley, K. Falconer, V. Kannan, and V. Kumar. This is the Proceedings of a conference on Fractals and Wavelets held in Kochi, India in 2013.

TOPOLOGICAL DYNAMICS AND TOPOLOGICAL DATA ANALYSIS

Springer, ISBN 978-981-16-0173-6, 2021. Coedited with K. Chan and V. Kumar. This is the Proceedings of a conference on Topological Dynamics and Topological Data Analysis held in Kochi, India in 2018.

COMPLEX DYNAMICS: TWENTY-FIVE YEARS AFTER THE APPEARANCE OF THE MANDELBROT SET

American Mathematical Society, ISBN 0-8218-3625-0. Contemporary Mathematics, 396, 2006. Coedited with L. Keen. This is the Proceedings of a conference on Complex Dynamics held at Snowbird, Utah, June 13-17, 2004.

CHAOS AND FRACTALS: THE MATHEMATICS BEHIND THE COMPUTER GRAPHICS.

Proceedings of the Symposia in Applied Mathematics, Vol. 39, American Mathematical Society, Providence, RI. ISBN 0-8218-0137-6.

This volume, coedited with Linda Keen, is a collection of papers delivered at the Short Course on Chaos and Fractals at the centennial meeting of the AMS in Providence, RI in 1988. Included are elementary papers on various topics in dynamics by: Philip J. Holmes, Kathleen T. Alligood and James A. Yorke, Linda Keen, Bodil Branner, Jenny Harrison, Michael F. Barnsley, and myself.

COMPLEX DYNAMICAL SYSTEMS: THE MATHEMATICS BEHIND THE MANDELBROT AND JULIA SETS

Proceedings of the Symposia in Applied Mathematics, Vol. 49, American Mathematical Society, Providence, RI. ISBN 0-8218-0290-9.

This volume contains a collection of papers delivered at the American Mathematical Society's Short Course on Complex Analytic Dynamics held at the annual AMS meeting in Cincinnati, OH in January, 1994. Included are papers by Bodil Branner, Linda Keen, Adrien Douady, Paul Blanchard, John Hubbard and Dierk Schleicher, and myself. Taken together, these papers represent a survey of the state of research back in the 1990's in this area of mathematics.

Complete list of publications.