The 1/2-Complex Bruno Function and the Yoccoz Function: A Numerical Study of the Marmi-Moussa-Yoccoz Conjecture

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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{M} = M_T ∪ M_S. We use this algorithm to test the Marmi-Moussa-Yoccoz Conjecture about the Holder continuity of the function z → −iB(z) + logU(e^{2πiz}) on {z ∈ C : z ≥ 0}, where 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].
    Original languageEnglish
    Pages (from-to)491-506
    Number of pages16
    JournalExperimental Mathematics
    Volume12
    Issue number4
    Publication statusPublished - 2003

    Keywords

    • Littlewood-Paley dyadic decomposition
    • Farey series
    • continued fraction
    • Complex Bruno Function
    • linearization of quadratic polynomial
    • Yoccoz Function

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