科研之友
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摘要
We show that the fast escaping set A(f) of a transcendental entire function f has a structure known as a spider's web whenever the maximum modulus of f grows below a certain rate. The proof uses a new local version of the cos pi rho theorem, based on a comparatively unknown result of Bending. We also give examples of entire functions for which the fast escaping set is not a spider's web which show that this growth rate is sharp. These are the first examples for which the escaping set has a spider's web structure but the fast escaping set does not. Our results give new insight into possible approaches to proving a conjecture of Baker, and also a conjecture of Eremenko.
- 出版日期2013-9-10
