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

Lipeomorphic equivalence for p-adic analytic functions: a comparison between complex and p-adic dynamics