Monday, October 22, 2012

1210.5384 (Davoud Cheraghi et al.)

A Proof of the Marmi-Moussa-Yoccoz conjecture for rotation numbers of
high type

Davoud Cheraghi, Arnaud Chéritat
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 H\"older 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.
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