Treffer: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Title:
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Publisher Information:
Taylor \& Francis, Philadelphia, PA
Subject Terms:
Maximal functions, Littlewood-Paley theory, Continued fractions, Relations of ergodic theory with number theory and harmonic analysis, Small divisors, rotation domains and linearization in holomorphic dynamics, Approximation methods and numerical treatment of dynamical systems, Dynamics of complex polynomials, rational maps, entire and meromorphic functions, Fatou and Julia sets
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
DOI:
10.1080/10586458.2003.10504517
Access URL:
Accession Number:
edsair.c2b0b933574d..6d0f39da00df4a6684486dc16ab70d7b
Database:
OpenAIRE
Weitere Informationen
Summary: 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 Hölder continuity of the function \(z\mapsto -i\mathbb{B}(z)+ \log U\!\left(e^{2\pi i z}\right)\) on \(\{ z\in \mathbb{C}: \Im z \geq 0 \}\), where \(\mathbb{B}\) is the \(1/2\)-complex Bruno function and \(U\) is the Yoccoz function. We give a positive answer to an explicit question of \textit{S. Marmi, P. Moussa} and \textit{J.-C. Yoccoz} [Commun. Math. Phys. 186, No. 2, 265--293 (1997; Zbl 0947.30018)].