# A Geometric Setting for Hamiltonian Perturbation Theory

, by
Note: Supplemental materials are not guaranteed with Rental or Used book purchases.
• ISBN: 9780821827208 | 0821827200
• Cover: Paperback
• ## Rent Textbook

(Recommended)

## Summary

Introduction Part 1. Dynamics: Lie-Theoretic preliminaries Action-group coordinates On the existence of action-group coordinates Naive averaging An abstract formulation of Nekhoroshev's theorem Applying the abstract Nekhoroshev's theorem to action-group coordinates Nekhoroshev-type estimates for momentum maps Part 2. Geometry: On Hamiltonian $G$-spaces with regular momenta Action-group coordinates as a symplectic cross-section Constructing action-group coordinates The axisymmetric Euler-Poinsot rigid body Passing from dynamic integrability to geometric integrability Concluding remarks Appendix A. Proof of the Nekhoroshev-Lochak theorem Appendix B. Proof the ${\mathcal W}$ is a slice Appendix C. Proof of the extension lemma Appendix D. An application of converting dynamic integrability into geometric integrability: The Euler-Poinsot rigid body revisited Appendix E. Dual pairs, leaf correspondence, and symplectic reduction Bibliography