A new geometric characterization of the Julia set

preprint2015arXivOpen access

This article concerns a new geometric characterization of the Julia set. By using Ahlfors-Shimizu's characteristic, we establish some growth results which indicates the characterization of the Julia set. The main technique is to estimate the lower bound of $S(f^n,U)$ , where $U$ is an open neighbourhood of some point in $\mathcal{J}(f)$ .

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A new geometric characterization of the Julia set

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