The Perturbation of Hamiltonian Systems with a Non-Abelian Symmetry

Citation

Blaom, Anthony David (1998) The Perturbation of Hamiltonian Systems with a Non-Abelian Symmetry. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/refg-y469. https://resolver.caltech.edu/CaltechTHESIS:07252025-175651501

Abstract

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 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.

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