- Young, Lai-Sang -- Special Topics in Analysis (Dynamical Systems and Ergodic Theory) (G)
- Stable and Random Motions in Dynamical Systems
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Young, Lai-Sang -- Special Topics in Analysis (Dynamical Systems and Ergodic Theory) (G)
Collected papers by Fritz John Book 6 editions published in in English and held by WorldCat member libraries worldwide. L Siegel Book 9 editions published between and in English and held by WorldCat member libraries worldwide. Calculus of variations : with supplementary notes and exercises, by Richard Courant Book 20 editions published between and in English and Undetermined and held by WorldCat member libraries worldwide.
The demand for a new edition and for an English translation gave rise to the present volume which, however, goes beyond a mere translation. To take account of recent work in this field a number of sections have been added, especially in the third chapter which deals with the stability theory. Still, it has not been attempted to give a complete presentation of the subject, and the basic prganization of Siegel's original book has not been altered.
Stable and Random Motions in Dynamical Systems
The emphasis lies in the development of results and analytic methods which are based on the ideas of H. Poincare, G. Birkhoff, A. Liapunov and, as far as Chapter I is concerned, on the work of K.
- Homoclinic orbits for the perturbed sine‐Gordon equation.
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- The global flow of the parabolic restricted three-body problem;
Sundman and C. In recent years the measure-theoretical aspects of mechanics have been revitalized and have led to new results which will not be discussed here. In this connection we refer, in particular, to the interesting book by V.
Arnold and A. Avez on "Problemes Ergodiques de la Mecanique Classique", which stresses the interaction of ergodic theory and mechanics. 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. 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. Foreward ix I.
The stability problem 3 2. Historical comments 3 3. Other problems 8 4. Unstable and statistical behavior 14 5. Plan 18 II. A model problem in the complex 21 2. Normal forms for Hamiltonian and reversible systems 30 3. Invariant manifolds 38 4. Twist theorem 50 III. Bernoulli shift.