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• W2092835880 abstract "We formulate Euler-Poincare equations on the Lie group Aut(P) of automorphisms of a principal bundle P. The corresponding flows are referred to as EPAut flows. We mainly focus on geodesic flows associated to Lagrangians of Kaluza-Klein type. In the special case of a trivial bundle P, we identify geodesics on certain infinite-dimensional semidirect-product Lie groups that emerge naturally from the construction. This approach leads naturally to a dual pair structure containing delta-like momentum map solutions that extend previous results on geodesic flows on the diffeomorphism group (EPDiff). In the second part, we consider incompressible flows on the Lie group of volume-preserving automorphisms of a principal bundle. In this context, the dual pair construction requires the definition of chromomorphism groups, i.e. suitable Lie group extensions generalizing the quantomorphism group." @default.
• W2092835880 created "2016-06-24" @default.
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• W2092835880 date "2010-06-03" @default.
• W2092835880 modified "2023-10-18" @default.
• W2092835880 title "Geometric dynamics on the automorphism group of principal bundles: geodesic flows, dual pairs and chromomorphism groups" @default.
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