Abstract
If ?A is an irrational number, Yoccoz defined the Brjuno function ?µ by ?µ(?A) =niÝ0 ?A0?A1 i? i? i? ?An.1 log 1 ?An , where ?A0 is the fractional part of ?A and ?An+1 is the fractional part of 1/?An. The numbers ?A such that ?µ(?A) < +iÞ are called the Brjuno numbers. The quadratic polynomial P?A : z iu e2i?Ð?Az + z2 has an indifferent fixed point at the origin. If P?A is linearizable, we let r(?A) be the conformal radius of the Siegel disk and we set r(?A) = 0 otherwise. Yoccoz [Y] proved that ?µ(?A) = +iÞ if and only if r(?A) = 0 and that the restriction of ?A iu ?µ(?A) + log r(?A) to the set of Brjuno numbers is bounded from below by a universal constant. In [BC2], we proved that it is also bounded from above by a universal constant. In fact, Marmi, Moussa and Yoccoz [MMY] conjecture that this function extends to R as a Hi§older function of exponent 1/2. In this article, we prove that there is a continuous extension to R.
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