Scaling Ratios and Triangles in Siegel Disks

Xavier Buff, Christian Henriksen

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    Abstract

    Let f(z)=e^{2i\pi \theta} + z^2, where \theta is a quadratic irrational. McMullen proved that the Siegel disk for f is self-similar about the critical point, and we show that if \theta = (\sqrt{5}-1)/2 is the golden mean, then there exists a triangle contained in the Siegel disk, and with one vertex at the critical point. This answers a 15 years old conjecture
    Original languageEnglish
    JournalMathematical Research Letters
    Volume6
    Issue number3-4
    Pages (from-to)293-305
    ISSN1073-2780
    Publication statusPublished - 1999

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