The Fatou–Julia theory for rational functions has been extended both to transcendental meromorphic functions and more recently to several different types of quasiregular mappings in higher dimensions. We extend the iterative theory to quasimeromorphic mappings with an essential singularity at infinity and at least one pole, constructing the Julia set for these maps. We show that this Julia set shares many properties with those for transcendental meromorphic functions and for quasiregular mappings of punctured space.

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关于拟亚纯映射的迭代

有理函数的 Fatou-Julia 理论已经扩展到超越亚纯函数，最近扩展到了几种不同类型的高维拟正则映射。我们将迭代理论扩展到在无穷远处具有本质奇点和至少一个极点的准亚纯映射，为这些映射构建 Julia 集。我们表明，这个 Julia 集与超越亚纯函数和穿孔空间的拟正则映射具有许多属性。