| Uniformly bounded components of normality (2007) | |||||||||
Abstract | |||||||||
| Suppose that $f(z)$ is a transcendental entire function and that the Fatou set $F(f)\neq\emptyset$. Set $$B_1(f):=\sup_{U}\frac{\sup_{z\in U}\log(|z|+3)}{\inf_{w\in U}\log(|w|+3)}$$ and $$B_2(f):=\sup_{U}\frac{\sup_{z\in U}\log\log(|z|+30)}{\inf_{w\in U}\log(|w|+3)},$$ where the supremum $\sup_{U}$ is taken over all components of $F(f)$. If $B_1(f). Comment: 17 pages, a revised version, to appear in Mathematical Proceedings Cambridge Philosophical Society | |||||||||
Publication details | |||||||||
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