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Titlebook: Geometry, Mechanics, and Dynamics; The Legacy of Jerry Dong Eui Chang,Darryl D. Holm,Tudor Ratiu Book 2015 Springer Science+Business Media

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Duncan Thomas McGuire,Gregory Ian Bainnterparts of symplectic groupoids, we describe “higher” versions of Poisson structures by identifying the infinitesimal counterparts of multisymplectic groupoids. Some basic examples and features are discussed.
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https://doi.org/10.1007/978-1-4899-6936-1 of automorphisms of a trivial principal bundle, generically called here non-abelian fluids. It is shown that the actions involved are mutually completely orthogonal, which directly implies the dual pair property.
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Dual Pairs for Non-Abelian Fluids, of automorphisms of a trivial principal bundle, generically called here non-abelian fluids. It is shown that the actions involved are mutually completely orthogonal, which directly implies the dual pair property.
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Polite Actions of Non-compact Lie Groups,general notion than properness of a group action, but also to more fully understand the role of invariant functions in describing just about everything of interest in reduction.We show that a polite action of a symmetry group of a dynamical system admits reduction and reconstruction.
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