论文标题

Speiser级朱莉娅(Julia)设置,尺寸接近一个

Speiser class Julia sets with dimension near one

论文作者

Bishop, Christopher J., Albrecht, Simon

论文摘要

对于任何$δ> 0 $,我们构建一个整个函数$ f $,带有三个单数值,其朱莉娅设置的hausdorff尺寸最多$ 1 =δ$。 Stallard证明,每当$ f $具有有限的单数集时,尺寸必须严格大于1,但是没有有限的单数集和尺寸的示例严格少于2个。

For any $ δ>0$ we construct an entire function $f$ with three singular values whose Julia set has Hausdorff dimension at most $1=δ$. Stallard proved that the dimension must be strictly larger than 1 whenever $f$ has a bounded singular set, but no examples with finite singular set and dimension strictly less than 2 were previously known.

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