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A geometric setting for Hamiltonian perturbation theory
About this Title
Anthony D. Blaom
Publication: Memoirs of the American Mathematical Society
Publication Year:
2001; Volume 153, Number 727
ISBNs: 978-0-8218-2720-8 (print); 978-1-4704-0320-1 (online)
DOI: https://doi.org/10.1090/memo/0727
MathSciNet review: 1848237
MSC: Primary 37J40; Secondary 37J15, 70G45, 70H06, 70H08, 70H09, 70H33
Table of Contents
Chapters
- Introduction
- Part 1. Dynamics
- 1. Lie-theoretic preliminaries
- 2. Action-group coordinates
- 3. On the existence of action-group coordinates
- 4. Naive averaging
- 5. An abstract formulation of Nekhoroshev’s theorem
- 6. Applying the abstract Nekhoroshev theorem to action-group coordinates
- 7. Nekhoroshev-type estimates for momentum maps
- Part 2. Geometry
- 8. On Hamiltonian $G$-spaces with regular momenta
- 9. Action-group coordinates as a symplectic cross-section
- 10. Constructing action-group coordinates
- 11. The axisymmetric Euler-Poinsot rigid body
- 12. Passing from dynamic integrability to geometric integrability
- 13. Concluding remarks