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.
Panorama
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.
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
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.