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Fractal dimension of Siegel disc boundaries

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Using renormalization techniques, we provide rigorous computer-assisted bounds on the Hausdorff dimension of the boundary of Siegel discs. Specifically, for Siegel discs with golden mean rotation number and quadratic critical points we show that the Hausdorff dimension is less than 1.08523. This is done by exploiting a previously found renormalization fixed point and expressing the Siegel disc boundary as the attractor of an associated Iterated Function System.
Original languageEnglish
Pages (from-to)263-265
Number of pages3
JournalThe European Physical Journal B
Volume4
Issue number3
DOIs
Publication statusPublished - 1998

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