seen in other completely integrable systems as was found before[@jose]. All in all the results shown in Fig.6 are consistent with what we have come to expect for the transition between regular and chaotic regions.

 Quasi-energy eigenfunction statistics
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Here we consider the statistical properties of the eigenfunction overlaps with the natural basis vectors. it has been conjectured [@alhassid] that as the classical motion changes from chaotic to regular, this distribution of overlaps can be represented by a $\chi^2$-distribution in $\nu$ degrees of freedom, with $\nu$ varying from 1 in the chaotic regime (the Porter-Thomas limit) to 0 in the regular region (the Poisson limit): $$P_{\nu}(y) = {(\nu /2)^{\nu /2}\over \Gamma (\nu /2)}
\enskip y^{\nu /2 -1}\enskip \exp(-\nu y/2).$$ Here $y \equiv \mid \langle\lambda |nl\rangle\mid ^2$, where $\mid{\lambda}\rangle$ label the QEF and $|{nl}\rangle$ label a set of $N$ orthogonal basis vectors. (The $y$’s have been rescaled so that $\langle{y}\rangle=1$.) We have tested this hypothesis for the overlap strengths for the same parameter values as for the quasi-energy eigenvalue statistics. The results are shown in Fig. 7, plotted on a logarithmic scale. These results show the general trend of decreasing $\nu$ as we cross the phase boundary from regular to chaotic 