WILD RECURRENT CRITICAL POINTS

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