  Marmi Moussa and Yoccoz conjectured that some error function Upsilon, related
to the approximation of the size of Siegel disk by some arithmetic function of
the rotation number theta, is a Holder continuous function of theta with
exponent 1/2. Using the renormalization invariant class of Inou and Shishikura,
we prove this conjecture for the restriction of Upsilon to a class of high type
numbers.
