In this paper it is shown that for a transcendental entire map with certain properties on the distribution of either its zeros, or points in its periodic and preperiodic Fatou domains, all of its Fatou components are simply connected, the union of its Julia set and \(\{ \infty \}\) is connected and the Julia set is uniformly perfect. Moreover, it is shown that any transcendental entire map that interpolates the 3n+1 problem has only simply connected Fatou components and its Julia set is uniformly perfect.

中文翻译：

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某些迭代整个映射的拓扑性质

本文表明，对于一个超越整个映射，其零点或周期和前周期 Fatou 域中的点的分布具有某些属性，它的所有 Fatou 分量都是简单连接的，其 Julia 集和\ (\{ \infty \}\)连通且 Julia 集一致完美。此外，还表明，插值 3n+1 问题的任何先验全图都只有简单连通的 Fatou 分量，并且其 Julia 集是一致完美的。