Distribution of rational maps with a preperiodic critical point
  Let {f_t} be any algebraic family of rational maps of a fixed degree, with a marked critical point c(t). We first prove that the hypersurfaces of parameters for which c(t) is periodic converge as a sequence of positive closed (1,1) currents to the bifurcation current attached to c and defined by DeMarco. We then turn our attention to the parameter space of polynomials of a fixed degree d. By intersecting the d-1 currents attached to each critical point of a polynomial, Bassaneli and Berteloot obtained a positive measure of finite mass which is supported on the connectedness locus. They showed that its support is included in the closure of the set of parameters admitting d-1 neutral cycles. We show that the support of this measure is precisely the closure of the set of strictly critically finite polynomials (i.e. of Misiurewicz points). 
Romain Dujardin and Charles Favre