A new geometric characterization of the Julia set

2015/12/16 by Xiao Yao, Yao, Xiao, Daochun Sun +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1512.05144

20 pages

arxiv created 2015/12/16 · arxiv updated 2015/12/17

Abstract

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(fⁿ,U), where U is an open neighbourhood of some point in J(f).

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