A Geometric Setting for Hamiltonian Perturbation Theory
American Mathematical Society (Verlag)
978-0-8218-2720-8 (ISBN)
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The perturbation theory of non-commutatively integrable systems is revisited from the point of view of non-Abelian symmetry groups. Using a coordinate system intrinsic to the geometry of the symmetry, we generalize and geometrize well-known estimates of Nekhoroshev (1977), in a class of systems having almost $G$-invariant Hamiltonians. These estimates are shown to have a natural interpretation in terms of momentum maps and co-adjoint orbits. The geometric framework adopted is described explicitly in examples, including the Euler-Poinsot rigid body.
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.
| Erscheint lt. Verlag | 1.9.2001 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Zusatzinfo | bibliography |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 255 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-8218-2720-0 / 0821827200 |
| ISBN-13 | 978-0-8218-2720-8 / 9780821827208 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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