Stable and Random Motions in Dynamical Systems: With Special Emphasis on Celestial Mechanics (Princeton Landmarks in Mathematics) [Paperback]

Jurgen Moser (Author)

Book Description

ISBN-10: 0691089108 | ISBN-13: 978-0691089102 | Publication Date: June 1, 2001

For centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Jürgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis. After thirty years, Moser's lectures are still one of the best entrées to the fascinating worlds of order and chaos in dynamics.

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About the Author

Daniel M. Kammen is Associate Professor of Energy and Society and director of the Renewable and Appropriate Energy Laboratory at the University of California, Berkeley. David M. Hassenzahl is Assistant Professor of Environmental Studies at the University of Nevada, Las Vegas. He has been an environmental risk professional in both the public and private sectors. Jurgen Moser, who died in 1999, was one of the most influential mathematicians of his generation. He made key contributions in dynamical systems and nonlinear analysis and was Director of the NYU Courant Institute, Director of the Research Institute for Mathematics at Switzerland's Federal Institute of Technology, and President of the International Mathematical Union. He received the 1994/95 Wolf Prize.

Product Details

• Paperback: 200 pages
• Publisher: Princeton University Press (June 1, 2001)
• Language: English
• ISBN-10: 0691089108
• ISBN-13: 978-0691089102
• Product Dimensions: 9.2 x 6.1 x 0.6 inches
• Shipping Weight: 8.8 ounces (View shipping rates and policies)
• Average Customer Review: 3.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,344,124 in Books (See Top 100 in Books)

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2 of 6 people found the following review helpful:

3.0 out of 5 stars Way above my head, unfortunately, January 28, 2007

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This review is from: Stable and Random Motions in Dynamical Systems: With Special Emphasis on Celestial Mechanics (Princeton Landmarks in Mathematics) (Paperback)

This book presents some of the research results for which Moser is famous. (He is the "M" of the KAM trio). The mathematical level is far too high for someone like me with only an introductory knowledge of differential equations and dynamical systems. This is not an introductory or expository work, but a reference for the research mathematician.