  We study ultrametric germs in one variable having an irrationally indifferent
fixed point at the origin with a prescribed multiplier. We show that for many
values of the multiplier, the cycles in the unit disk of the corresponding
monic quadratic polynomial are "optimal" in the following sense: They minimize
the distance to the origin among cycles of the same minimal period of
normalized germs having an irrationally indifferent fixed point at the origin
with the same multiplier. We also give examples of multipliers for which the
corresponding quadratic polynomial does not have optimal cycles. In those cases
we exhibit a higher degree polynomial such that all of its cycles are optimal.
The proof of these results reveals a connection between the geometric location
of periodic points of ultrametric power series and the lower ramification
numbers of wildly ramified field automorphisms. We also give an extension of
Sen's theorem on wildly ramified field automorphisms, and a characterization of
minimally ramified power series in terms of the iterative residue.
