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2003 The 1/2-Complex Bruno Function and the Yoccoz Function: A Numerical Study of the Marmi-Moussa-Yoccoz Conjecture
Timoteo Carletti
Experiment. Math. 12(4): 491-506 (2003).

Abstract

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].

Citation

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Timoteo Carletti. "The 1/2-Complex Bruno Function and the Yoccoz Function: A Numerical Study of the Marmi-Moussa-Yoccoz Conjecture." Experiment. Math. 12 (4) 491 - 506, 2003.

Information

Published: 2003
First available in Project Euclid: 18 June 2004

zbMATH: 1173.37324
MathSciNet: MR2043999

Subjects:
Primary: 37F50 , 42B25

Keywords: Complex Bruno Function , Continued fraction , Farey series , linearization of quadratic polynomial , Littlewood-Paley dyadic decomposition , Yoccoz Function

Rights: Copyright © 2003 A K Peters, Ltd.

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