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. We give examples of entire functions for which thefast escaping set is not a spider's web which show that this growth rate isbest possible. By our earlier results, these are the first examples for whichthe escaping set has a spider's web structure but the fast escaping set doesnot. These results give new insight into a conjecture of Baker and a conjectureof Eremenko.
展开▼
机译：我们表明，只要$ f $的最大模数低于某个速率，超验整个函数$ f $的快速转义集合$ A（f）$就会具有称为蜘蛛网的结构。我们给出了快速转义集合不是蜘蛛网的所有功能的示例，这些示例表明此增长率是最大的。根据我们较早的结果，这些是转义集合具有蜘蛛网结构但快速转义集合没有蜘蛛网结构的第一个示例。这些结果为贝克的猜想和埃雷缅科的猜想提供了新的见识。
展开▼
