A Geometric Setting For Hamiltonian Perturbation Theory

Download or read book A Geometric Setting for Hamiltonian Perturbation Theory written by Anthony D. Blaom and published by American Mathematical Soc.. This book was released on 2001 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, the perturbation theory of non-commutatively integrable systems is revisited from the point of view of non-Abelian symmetry groups. Using a co-ordinate system intrinsic to the geometry of the symmetry, the book generalizes and geometrizes 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.