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

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.

71 pages, pre publication version

References in corpus (3)

• Satellite renormalization of quadratic polynomials
• Typical orbits of quadratic polynomials with a neutral fixed point: Brjuno type
• The fixed point of the parabolic renormalization operator

Cited by in corpus (5)

• Satellite renormalization of quadratic polynomials
• The high type quadratic Siegel disks are Jordan domains
• Regularity properties of $k$-Brjuno and Wilton functions
• Dimension paradox of irrationally indifferent attractors
• The Brjuno functions of the by-excess, odd, even and odd-odd continued fractions and their regularity properties