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This article gives a first look at wild ramification in a family of iteratedextensions. For integer values of c, we consider the splitting field of $(x^2 +c)^2 + c$, the second iterate of $x^2 + c$. We give complete information on thefactorization of the ideal (2) as c varies, and find a surprisingly complicateddependence of this factorization on the parameter c. We show that 2 ramifies(necessarily wildly) in all these extensions except when c = 0, and we describethe higher ramification groups in some totally ramified cases.

Wild ramification in a family of low-degree extensions arising from iteration