Moser Stable and Random Motions in Dynamical Systems

With Special Emphasis on Celestial Mechanics (AM-77)
With a New foreword by Philip J. Holmes
ISBN: 978-1-4008-8269-4
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 31, 216 Seiten

Reihe: Princeton Landmarks in Mathematics and Physics

No detailed description available for "Stable and Random Motions in Dynamical Systems".

Autoren/Hrsg.

Moser, Jurgen

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Astrophysik

Inhaltsverzeichnis

Foreward ix

I. INTRODUCTION 3

1. The stability problem 3

2. Historical comments 3

3. Other problems 8

4. Unstable and statistical behavior 14

5. Plan 18

II. STABILITY PROBLEM 21

1. 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. STATISTICAL BEHAVIOR 61

1. Bernoulli shift. Example 61

2. Shift as a topological mapping 66

3. Shift as a subsystem 68

4. Alternate conditions for C'-mappings 76

5. The restricted three-body problem 83

6. Homoclinic points 99

IV. FINAL REMARKS 113

V. EXISTENCE PROOF IN THE PRESENCE OF SMALL DIVISORS 113

1. Reformulation of Theorem 2.9 113

2. Construction of the root of a function 120

3. Proof of Theorem 5.1 127

4. Generalities 138

A. Appendix to Chapter V 149

a. Rate of convergence for scheme of s.2b) 149

b. The improved scheme by Hald 151

VI. PROOFS AND DETAILS FOR CHAPTER III 153

1. Outline 153

2. Behavior near infinity 154

3. Proof of Lemmas 1 and 2 of Chapter III 160

4. Proof of Lemma 3 of Chapter III 163

5. Proof of Lemma 4 of Chapter III 167

6. Proof of Lemma 5 of Chapter III 171

7. Proof of Theorem 3.7, concerning homoclinic points 181

8. Nonexistence of intergals 188

BOOKS AND SURVEY ARTICLES 191

Über Autor(innen)

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's
Federal Institute of Technology, and President of the International Mathematical Union. He was awarded the 1994/95 Wolf Prize.