Dynamics: A First Course

With a Panorama of Recent Developments

By Anatole Katok and Boris Hasselblatt

Cambridge University Press, 2003. ISBN 0-521-58304-7

Paperback, 2003: ISBN 0-521-58750-6.

Russian translation: Publishing House MCCME, 2005


Errata — Please any errors you notice in the book.

This book provides a self-contained introductory course on dynamical systems for advanced undergraduate students as well as a selection of recent developments in dynamical systems that serve to illustrate applications and refinements of the ideas from this course. The parts differ fundamentally in pedagogical approach but are closely interrelated. Either part can stand on its own; the course is complete without the Panorama, and the Panorama does not require this specific course as background. Scientists and engineers can enjoy this book by picking and choosing, from both Panorama and the course text.


The book begins with an introduction to pique interest in dynamics and to present samples of what scientific and mathematical problems dynamics can address. It adds to the enjoyment of the course, but it is not a required part of it.

The course

The undergraduate course assumes only knowledge about linear maps and eigenvalues, multivariable differential calculus and Riemann integration with proofs. Some background is developed in Chapter 9 and the appendix. Dynamics provides the concepts and tools to describe and understand complex long-term behavior in systems that evolve in time. The course accordingly develops these ideas in a gradual progression towards ever greater complexity, with proofs. Both topological and statistical points of view are developed. We know of no other text that makes both accessible at the undergraduate level.


The Panorama of dynamical systems assumes slightly stronger mathematical background in some places, but this is balanced by a more relaxed standard of proof that serves to outline and explain further developments carefully without carrying all of them out. It provides applications of the ideas in the course and connects them to topics of current interest, including ample references in the text.

Further reading

The most natural continuation of the course presented here and of some subjects in the panorama is our book ``Introduction to the Modern Theory of Dynamical Systems'' (Cambridge University Press, 1995), which also provides some reading to complement this course. We offer reading suggestions at the end of the book.

Reviews of "Introduction To The Modern Theory Of Dynamical Systems" by the same authors

The authors...have a definite idea what dynamical systems theory is all about. A first rate text with more than enough dynamics to suit just about anyone's taste...carefully and masterfully written...a classic compendium. It is a must-have for any researcher in the field.
Robert Devaney, Mathematical Intelligencer
A comprehensive exposition. Seemingly every topic is covered in depth.
Matt Richey, American Mathematical Monthly
The book...is unique in giving a detailed presentation of a large part of smooth dynamics in a consistent style...unrivalled as a comprehensice introduction at an advanced level.
David Ruelle, Ergodic Theory and Dynamical Systems
Even specialists will find original aspects and new points of view...the mathematical examples play a prominent role, which I found very attractive...The treatment of hyperbolic systems, including their ergodic properties...is in my opinion really excellent. It is the most accessible treatment of this theory.
Floris Takens, Bulletin of the American Mathematical Society
Of the current flood of books on the subject, this one distinguishes itself in many ways...I recommend it also as an important source to all those involved in the interface between the mathematical theory and its increasingly pervasive role in the scientific world.
Robert MacKay, Bulletin of the London Mathematical Society
There is no other treatment coming close in terms of comprehensiveness and readability. It is indispensable for anybody working on dynamical systems in almost any context, and even experts will find interesting new proofs and historical references throughout the book.
Klaus Schmidt, Monatshefte für Mathematik
The notes section at the end of the book is complete and quite helpful. There are hints and answers provided for a good percentage of the problems in the book. The problems range from fairly straightforward ones to results that I remember reading in research papers over the last 10-20 years...I recommend the text as an exceptional reference.
Richard Swanson, SIAM Review
Meines Erachtens stellt Katok und Hasselblatts "Introduction to the modern theory of dynamical systems" eine äußerst wertvolle Bereicherung der Literatur über die Theorie dynamischer Systeme dar, und ich kann das Buch jedem uneingeschränkt empfehlen, der diese Theorie in Lehre oder Forschung behandelt oder anwendet.
Gerhard Sorger, International Mathematical News
This remarkable book is by far the best rigorous introduction to many facets of the modern theory of (chaotic) dynamical systems. It introduces and rigorously develops the central concepts and methods in dynamical systems in a hands-on and highly insightful fashion. The authors are world experts in smooth dynamical systems and have played a major role in the development of the modern theory and this shows througout the book. This book should be on the desk (not bookshelf!) of any serious student of dynamical systems or any mathematically sophisticated scientist or engineer interested in using tools and paradigms of dynamical systems to model or study nonlinear systems.
A reader, Amazon.com
Well written and clear...a valuable reference for engineers and mechanicians.
Henry W. Haslach, Applied Mechanics Review
The book is a pleasure to read.
Edoh Amiran, Mathematical Reviews

Further reading



Georg Cantor
Mary Lucy Cartwright
Mary Lucy Cartwright
Steven Smale
George David Birkhoff

The picture shows the authors in Oberwolfach (1997). Photograph by Krystyna Kuperberg.