$T=1.0$, $p_0=0.0$

Figures 5.9-5.11 and C.41-C.46.

As discussed in section 5.2, the experience gained while numerically iterating the quantum map for many different combinations of parameters and initial states indicates that in the case of localization the dynamics is ``robust'' with respect to the initial state: having iterated just long enough, for a given parameter combination always the same type of quantum dynamics evolves, regardless of the exact choice of $\left\vert \psi_0 \right>$: rotation around the phase space origin, with the HUSIMI distribution essentially nonzero only in an annular area that includes the location of the initial $F^{\rm H}(x,p,-0;1)$.

Note that there are indications of quantum revivals [BL57,YMS90,AP89] -- see for example figure C.41, $n=1000/10000$ and $n=300/100000$; many more examples can be identified in the numerically collected data. I do not discuss this feature any further here.