  Let K be a p-adic field, and suppose that f and g are germs of analytic
functions on K which are tangent to the identity at 0. It is known that f and g
are homeomorphically equivalent, meaning there is an invertible germ h
conjugating f to g. In this paper, we determine whether there exists such h
which are lipeomorphisms, and moreover find the best possible Holder estimate
at 0. Our results have striking complex and real counterparts.
