Contents
Abstract viii
Notation ix
Overture xii
Introduction 1
Part 1. Dynamics 7
Chapter 1. Lie-Theoretic Preliminaries 8
Chapter 2. Action-Group Coordinates 10
Chapter 3. On the Existence of Action-Group Coordinates 15
Chapter 4. Naive Averaging 21
Chapter 5. An Abstract Formulation of Nekhoroshev's Theorem 26
Chapter 6. Applying the Abstract Nekhoroshev Theorem to Action-
Group Coordinates 31
Chapter 7. Nekhoroshev-Type Estimates for Momentum Maps 42
Part 2. Geometry 45
Chapter 8. On Hamiltonian G-Spaces with Regular Momenta 46
Chapter 9. Action-Group Coordinates as a Symplectic Cross-Section 53
Chapter 10. Constructing Action-Group Coordinates 58
Chapter 11. The Axisymmetric Euler-Poinsot Rigid Body 65
Chapter 12. Passing from Dynamic Integrability to Geometric
Integrability 70
Chapter 13. Concluding Remarks 75
Appendix A. Proof of the Nekhoroshev-Lochak Theorem 77
Appendix B. Proof that W is a Slice 92
Appendix C. Proof of the Extension Lemma 93
Appendix D. An Application of Converting Dynamic Integrability
into Geometric Integrability: The Euler-Poinsot Rigid
Body Revisited 95
Appendix E. Dual Pairs, Leaf Correspondence, and Symplectic
Reduction 100
Bibliography 110
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