We show that for any quasimeromorphic mapping with an essential singularity at infinity, there exist points whose iterates tend to infinity arbitrarily slowly. This extends a result by Nicks for quasiregular mappings, and Rippon and Stallard for transcendental meromorphic functions on the complex plane. We further establish a new result for the growth rate of quasiregular mappings near an essential singularity, and briefly extend some results regarding the bounded orbit set and the bungee set to the quasimeromorphic setting.

中文翻译：

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关于准亚纯映射的慢转义点和非转义点

我们证明，对于任何在无穷远处具有本质奇点的拟亚纯映射，都存在迭代趋向于任意缓慢地无穷大的点。这扩展了 Nicks 对拟正则映射的结果，以及 Rippon 和 Stallard 对复平面上的超越亚纯函数的结果。我们进一步建立了一个本质奇点附近准正则映射增长率的新结果，并将一些关于有界轨道集和蹦极集的结果简单地推广到了准亚纯态。