03-248 Timoteo Carletti

The $1/2$--Complex Bruno function and the Yoccoz function. A numerical study of the Marmi--Moussa--Yoccoz Conjecture. (6259K, postscript file) May 30, 03

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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}.

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