Self-similarity of Siegel Disks and Hausdorr Dimension of Julia Sets
نویسنده
چکیده
Let f (z) = e 2ii z + z 2 , where is an irrational number of bounded type. According to Siegel, f is linearizable on a disk containing the origin. In this paper we show: the Hausdorr dimension of the Julia set J (f) is strictly less than two; and if is a quadratic irrational (such as the golden mean), then the Siegel disk for f is self-similar about the critical point. In the latter case, we also show the rescaled rst-return maps converge exponentially fast to a system of commuting branched coverings of the complex plane.
منابع مشابه
Self-similarity of Siegel disks and Hausdorff dimension of Julia sets
Let f(z) = ez + z, where θ is an irrational number of bounded type. According to Siegel, f is linearizable on a disk containing the origin. In this paper we show: • the Hausdorff dimension of the Julia set J(f) is strictly less than two; and • if θ is a quadratic irrational (such as the golden mean), then the Siegel disk for f is self-similar about the critical point. In the latter case, we als...
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