On gauge Poisson brackets with prescribed symmetry (Q6601048)

This paper describes a reconstruction of invariant connection-dependent Poisson structures from canonical actions of compact Lie groups. First, the authors recall some facts about gauge Poisson brackets on trivial Poisson bundles. Properties of Wong's system and its generalizations are given in the context of Hamiltonian dynamics. Then, the authors describe a class of G-invariant gauge Poisson structures and Wong's type equations. They also apply a coordinate-free approach to obtain a class of generalized Wong's equations on non-trivial Lie-Poisson bundles equipped with a class of fiberwise linear gauge Poisson brackets associated to Lie algebroids.