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Book DetailsColloquium PublicationsVolume: 9; 1927; 305 ppMSC: Primary 34;
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.ReadershipGraduate students and research mathematicians interested in dynamical systems.
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Table of Contents
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Chapters
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Chapter I. Physical aspects of dynamical systems
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Chapter II. Variational principles and applications
-
Chapter III. Formal aspects of dynamics
-
Chapter IV. Stability of periodic motions
-
Chapter V. Existence of periodic motions
-
Chapter VI. Application of Poincaré’s geometric theorem
-
Chapter VII. General theory of dynamical systems
-
Chapter VIII. The case of two degrees of freedom
-
Chapter IX. The problem of three bodies
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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.
Graduate students and research mathematicians interested in dynamical systems.
-
Chapters
-
Chapter I. Physical aspects of dynamical systems
-
Chapter II. Variational principles and applications
-
Chapter III. Formal aspects of dynamics
-
Chapter IV. Stability of periodic motions
-
Chapter V. Existence of periodic motions
-
Chapter VI. Application of Poincaré’s geometric theorem
-
Chapter VII. General theory of dynamical systems
-
Chapter VIII. The case of two degrees of freedom
-
Chapter IX. The problem of three bodies
