Abstract
We investigate the reduction and unfolding of dynamical systems with gauge symmetries. An application is provided by a non relativistic point charge in the field of a Dirac monopole. The corresponding dynamical system possessing a Kepler type symmetry is associated with the Taub-NUT metric using a reduction procedure of symplectic manifolds with symmetries. The reverse of the reduction procedure is done by stages performing the unfolding of the gauge transformation followed by the Eisenhart lift in connection with scalar potentials.
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