Stable and Random Motions in Dynamical Systems: With Special Emphasis on Celestial Mechanics (AM-77) (Princeton Landmarks in Mathematics and Physics, 38) by Jurgen Moser (PDF)

Description

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.

User’s Reviews

Editorial Reviews: About the Author Jürgen Moser, who died in 1999, was one of the most influential mathematicians of his generation, making important contributions in dynamical systems and nonlinear analysis. Among other posts, he was variously Director of the New York University Courant Institute, Director of the Research Institute for Mathematics at Switzerland’sFederal Institute of Technology, and President of the International Mathematical Union. He was awarded the 1994/95 Wolf Prize.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐Un magnifique livre de mathématique de haut niveau écrit dans un style abordable par le non spécialiste. L’auteur est un des trois mathématiciens immortalisés par l’acronyme “KAM”. Un aspect fascinant de la théorie KAM est la manière dont les dynamiques elliptiques et hyperboliques s’entremêlent à toutes les échelles de l’espace des phases. Dans ce livre, Moser se concentre sur la partie hyperbolique en revisitant (en particulier) le théorème du fer à cheval de Smale.

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