  We calculate the atomic (spin) Wigner function for the single mode Dicke
model in the regime of large number of two-level atoms. The dynamics of this
quasi-probability function on the Bloch sphere allows us to visualize the
consequences of the entanglement process between the boson and the spin
subsystems. Such investigation shows a distinct localization behavior of the
spin state with respect to the polar and azimuthal Bloch sphere angles. A
complete {\em breakdown of reflection symmetry} in the azimuthal angle is shown
in the non-integrable case, even at short evolution times. Also, in the
classically chaotic situation, the appearance of {\em sub-planck structures} in
the Wigner function is shown, and its evolution analyzed.
