We study the 1/2-Complex Bruno function and we produce an algorithm to evaluate it numerically, giving a characterization of the monoid {\small $\hat{\mathcal{M}}=\mathcal{M}_T\cup \mathcal{M}_S$}. We use this algorithm to test the
Marmi-Moussa-Yoccoz Conjecture about the Holder continuity of the function {\small $z\mapsto -i\B(z)+ \log U\!\left(e^{2\pi i
z}\right)$} on {\small $\{ z\in \C: \Im z \geq 0 \}$}, where {\small $\B$} 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 [Marmi et al. 01].
Publié le : 2003-05-14
Classification:
Complex Bruno Function,
Yoccoz Function,
linearization of quadratic polynomial,
Littlewood-Paley dyadic decomposition,
continued fraction,
Farey series,
37F50,
42B25
@article{1087568025,
author = {Carletti, Timoteo},
title = {The 1/2-Complex Bruno Function and the Yoccoz Function: A Numerical Study of the Marmi-Moussa-Yoccoz Conjecture},
journal = {Experiment. Math.},
volume = {12},
number = {1},
year = {2003},
pages = { 491-506},
language = {en},
url = {http://dml.mathdoc.fr/item/1087568025}
}
Carletti, Timoteo. The 1/2-Complex Bruno Function and the Yoccoz Function: A Numerical Study of the Marmi-Moussa-Yoccoz Conjecture. Experiment. Math., Tome 12 (2003) no. 1, pp. 491-506. http://gdmltest.u-ga.fr/item/1087568025/