A Sharp Growth Condition for a Fast Escaping Spider’s Web
نویسندگان
چکیده
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 the fast escaping set is not a spider’s web which show that this growth rate is best possible. By our earlier results, these are the first examples for which the escaping set has a spider’s web structure but the fast escaping set does not. These results give new insight into a conjecture of Baker and a conjecture of Eremenko.
منابع مشابه
The structure of spider’s web fast escaping sets
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We construct several new classes of transcendental entire functions, f , such that both the escaping set, I ( f ), and the fast escaping set, A( f ), have a structure known as a spider’s web. We show that some of these classes have a degree of stability under changes in the function. We show that new examples of functions for which I ( f ) and A( f ) are spiders’ webs can be constructed by comp...
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