Let K be an algebraically closed field that is complete with respect to a non-Archimedean absolute value, and let φ ∈ K(z) have degree d ≥ 2. We characterize maps for which the minimal resultant of an iterate φⁿ is given by a simple formula in terms of d, n, and the minimal resultant of φ. Three characterizations of such maps are given, one measure-theoretic and two in terms of the indeterminacy locus I(d) in the parameter space P^2d+1 of (possibly degenerate) rational maps. As an application, we are able to give a new explicit formula involving the Arakelov-Green's function attached to φ. We end by illustrating our results with some explicit examples.

The authors would like to thank Laura DeMarco and Matt Baker for helpful coorespondence in preparing this manuscript, along with the anonymous referees for feedback on earlier drafts.