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arXiv · 1210.5384

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

Davoud Cheraghi·Arnaud Chéritat
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Abstract

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.

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Davoud Cheraghi, Arnaud Chéritat. 2012-10-19. A Proof of the Marmi-Moussa-Yoccoz conjecture for rotation numbers of high type. https://doi.org/10.1007/s00222-014-0576-2

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