Timoteo Carletti
The $1/2$--Complex Bruno function and the Yoccoz function. 
A numerical study of the Marmi--Moussa--Yoccoz Conjecture.
(6259K, postscript file)

ABSTRACT.  We study the $1/2$--Complex Bruno function and we produce an algorithm 
to evaluate it numerically, giving a characterization of the 
monoid $\hat{\mathcal{M}}=\mathcal{M}_T\cup \mathcal{M}_S$. 
We use this algorithm to test the Marmi--Moussa--Yoccoz Conjecture about the 
H\"older continuity of the function $z\mapsto -i\mathbf{B}(z)+ 
\log U\!\left(e^{2\pi i z}\right)$ on $\{ z\in \mathbb{C}: \Im z \geq 0 \}$, where $\mathbf{B}$ is the $1/2$--complex 
Bruno function and $U$ is the Yoccoz function. We give a positive 
answer to an explicit question of S. Marmi et al~\cite{MMYc}.