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This paper develops the theory of affine Lie-Poisson reduction and applies this process to Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids. As a consequence of this approach, the associated Poisson brackets are obtained by reduction of a canonical cotangent bundle. A Kelvin-Noether circulation theorem is presented and is applied to these examples.
Jan Sickmann Hesthaven, Nicolò Ripamonti, Cecilia Pagliantini
Pablo Antolin Sanchez, Ondine Gabrielle Chanon