A new geometric characterization of the Julia set

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 $S(f^n,U)$, where $U$ is an open neighbourhood of some point in $\mathcal{J}(f)$.

20 pages

Cited by in corpus (1)

• Lyapunov exponents and related concepts for entire functions