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Wiman–Valiron Discs and the Dimension of Julia Sets
International Mathematics Research Notices ( IF 1 ) Pub Date : 2020-03-03 , DOI: 10.1093/imrn/rnaa029
James Waterman 1
Affiliation  

We show that the Hausdorff dimension of the set of points of bounded orbit in the Julia set of a meromorphic map with a simply connected direct tract and a certain restriction on the singular values is strictly greater than one. This result is obtained by proving new results related to Wiman-Valiron theory.

中文翻译:

Wiman-Valiron 圆盘和 Julia 集的维数

我们证明了具有简单连接的直接道和对奇异值的某些限制的亚纯映射的 Julia 集中的有界轨道点集的 Hausdorff 维数严格大于 1。该结果是通过证明与 Wiman-Valiron 理论相关的新结果而获得的。
更新日期:2020-03-03
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