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arXiv · 1912.12005

On the iterations and the argument distribution of meromorphic functions

Jianhua Zheng·Jie Ding
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Abstract

This paper consists of tow parts. One is to study the existence of a point $a$ in the intersection of Julia set and escaping set such that $\arg z=\theta$ is a singular direction if $\theta$ is a limit point of $\{\arg f^n(a)\}$ under some growth condition of a meromorphic function. The other is to study the connection between the Fatou set and singular direction. We prove that the absent of singular direction deduces the non-existence of annuli in the Fatou set.

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Jianhua Zheng, Jie Ding. 2019-12-27. On the iterations and the argument distribution of meromorphic functions. https://arxiv.org/abs/1912.12005

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