  We use the Barnett-Pegg formalism of angle operators to study a rotating
particle with and without a flux line. Requiring a finite dimensional version
of the Wigner function to be well defined we find a natural time quantization
that leads to classical maps from which the arithmetical basis of quantum
revivals is seen. The flux line, that fundamentally alters the quantum
statistics, forces this time quantum to be increased by a factor of a winding
number and determines the homotopy class of the path. The value of the flux is
restricted to the rational numbers, a feature that persists in the infinite
dimensional limit.
