Colloquium Publications
Volume: 9;
1927;
305 pp;
Softcover
MSC: Primary 34;
Print ISBN: 978-0-8218-1009-5
Product Code: COLL/9
List Price: $66.00
AMS Member Price: $52.80
MAA Member Price: $59.40
Electronic ISBN: 978-0-8218-3394-0
Product Code: COLL/9.E
List Price: $66.00
AMS Member Price: $52.80
MAA Member Price: $59.40
Dynamical Systems
Share this pageGeorge D. Birkhoff
His research in dynamics constitutes the middle period of Birkhoff's scientific career, that of maturity and greatest power.
—Yearbook of the American Philosophical Society
The author's great book…is well known to all, and the diverse active modern developments in mathematics which have been inspired by this volume bear the most eloquent testimony to its quality and influence.
—Zentralblatt MATH
In 1927, G. D. Birkhoff wrote a remarkable treatise on the theory of
dynamical systems that would inspire many later mathematicians to do great
work. To a large extent, Birkhoff was writing about his own work on the
subject, which was itself strongly influenced by Poincaré's approach to
dynamical systems. With this book, Birkhoff also demonstrated that the
subject was a beautiful theory, much more than a compendium of individual
results. The influence of this work can be found in many fields, including
differential equations, mathematical physics, and even what is now known
as Morse theory.
The present volume is the revised 1966 reprinting of the book,
including a new addendum, some footnotes, references added by Jürgen
Moser, and a special preface by Marston Morse.
Although dynamical systems has thrived in the decades since Birkhoff's
book was published, this treatise continues to offer insight and
inspiration for still more generations of mathematicians.
Readership
Graduate students and research mathematicians interested in dynamical systems.
Table of Contents
Table of Contents
Dynamical Systems
- Cover Cover11
- Title page i2
- Introduction to the 1966 Edition iii4
- Preface to the 1966 Edition iv5
- Preface to the 1927 Edition vi7
- Contents ix10
- Chapter I. Physical aspects of dynamical systems 114
- Chapter II. Variational principles and applications 3346
- Chapter III. Formal aspects of dynamics 5972
- Chapter IV. Stability of periodic motions 97110
- Chapter V. Existence of periodic motions 123136
- Chapter VI. Application of Poincaré’s geometric theorem 150163
- Chapter VII. General theory of dynamical systems 189202
- Chapter VIII. The case of two degrees of freedom 209222
- Chapter IX. The problem of three bodies 260273
- Addendum 293306
- Footnotes 296309
- Bibliography 300313
- Index 303316
- Back Cover Back Cover1319