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).

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.

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).

Want to see some happy readers of the first edition? Click here.

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.

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.

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).

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.

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.