  We focus on the frontier between the chaotic and regular regions for the
classical version of the quantum kicked top. We show that the sensitivity to
the initial conditions is numerically well characterised by $\xi=e_q^{\lambda_q
t}$, where $e_{q}^{x}\equiv [ 1+(1-q) x]^{\frac{1}{1-q}} (e_1^x=e^x)$, and
$\lambda_q$ is the $q$-generalization of the Lyapunov coefficient, a result
that is consistent with nonextensive statistical mechanics, based on the
entropy $S_q=(1- \sum_ip_i^q)/(q-1) (S_1 =-\sum_i p_i \ln p_i$). Our analysis
shows that $q$ monotonically increases from zero to unity when the kicked-top
perturbation parameter $\alpha $ increases from zero (unperturbed top) to
$\alpha_c$, where $\alpha_c \simeq 3.2$. The entropic index $q$ remains equal
to unity for $\alpha \ge \alpha_c$, parameter values for which the phase space
is fully chaotic.
