Misiurewicz maps unfold generically (even if they are critically non-finite)

We show that in normalized families of polynomial or rational maps, Misiurewicz maps (critically finite or infinite) unfold generically. For example, if f(lambda 0) is critically finite with non-degenerate critical point c(1)(lambda(0)),...,c(n)(lambda(0)) such that f(lambda 0)(ki) (c(i)(lambda(0))) = p(i)(lambda(0)) are hyperbolic periodic points for i = 1,..., n, then lambda --> (f(lambda)(k1)(c(1)(lambda)) - p(1)(lambda),...,f(lambda)(kd-2) (c(d-2)(lambda)) - p(d-2)(lambda)) is a local diffeomorphism for lambda near lambda(0). For quadratic families this result was proved previously in [DH] using entirely different methods