  It is conjectured that a rational map whose coefficients are algebraic over
$\Q_p$ has no wandering components of the Fatou set. R. Benedetto has shown
that any counter example to this conjecture must have a wild recurrent critical
point. We provide here the first examples of rational maps whose coefficients
are algebraic over $\Q_p$ and that have a (wild) recurrent critical point. In
fact, we show that there is such a rational map in every one parameter family
of rational maps that is defined over a finite extension of $\Q_p$ and that has
a Misiurewicz bifurcation.
