  We establish an approximation of the activity current $T_c$ in the parameter
space of a holomorphic family $f$ of rational functions having a marked
critical point $c$ by parameters for which $c$ is periodic under $f$, i.e., is
a superattracting periodic point. This partly generalizes a Dujardin--Favre
theorem for rational functions having preperiodic points, and refines a
Bassanelli--Berteloot theorem on a similar approximation of the bifurcation
current $T_f$ of the holomorphic family $f$. The proof is based on a dynamical
counterpart of this approximation.
