Dynamics with exotic symmetries

Inspired by the geometrical methods allowing the introduction of mechanical systems confined in the plane and endowed with exotic galilean symmetry, we resort to the Lagrange-Souriau 2-form formalism, in order to look for a wide class of 3D systems, involving not commuting and/or not canonical variables, but possessing geometric as well gauge symmetries in position and momenta space too. As a paradigmatic example, a charged particle simultaneously interacting with a magnetic monopole and a dual monopole in momenta space is considered. The main features of the motions, conservation laws and the analogies with the planar case are discussed. Possible physical realizations of the model are proposed.