Fractal dimension of Siegel disc boundaries

A. D. Burbanks; A. H. Osbaldestin; A. Stirnemann

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Fractal dimension of Siegel disc boundaries

机译：Siegel盘边界的分形维数

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摘要

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.

机译：使用重归一化技术，我们在Siegel圆盘边界的Hausdorff维度上提供了严格的计算机辅助范围。具体来说，对于具有黄金平均转数和二次临界点的Siegel圆盘，我们表明Hausdorff尺寸小于1.08523。这是通过利用先前找到的重归一化固定点并将Siegel圆盘边界表示为关联的迭代功能系统的吸引子来完成的。

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《Zeitschrift fur Physik, B. Condensed Matter》 |1998年第3期|共3页
作者
A. D. Burbanks; A. H. Osbaldestin; A. Stirnemann;
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正文语种 eng
中图分类物理学;
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05.45.+b theory and models of chaotic systems; 47.53.+n fractals;

机译：05.45。+ b混沌系统理论与模型;47.53。+ n分形;

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Fractal dimension of Siegel disc boundaries

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