The Perturbation of Hamiltonian Systems with a Non-Abelian Symmetry

Author: Blaom, Anthony David

Year: 1998

Degree: Dissertation (Ph.D.)

Advisors: Marsden, Jerrold E.; Luxemburg, W. A. J.

Committee Members: Marsden, Jerrold E.; Gabai, David; Ratiu, Tudor; Simon, Barry M.

Option: Mathematics

DOI: 10.7907/refg-y469

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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