This article gives a first look at wild ramification in a family of iterated extensions. For  we consider the splitting field of  the second iterate of  We give complete information on the factorization of the ideal (2) as c varies, and find a surprisingly complicated dependence of this factorization on the parameter c. We show that 2 ramifies (necessarily wildly) in all  these extensions except when  and we describe the higher ramification groups in some totally ramified cases.

ramification, number fields, polynomial iteration, ideal factorization.