Entire functions for which the escaping set is a spider's web

Abstract

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 composition, by differentiation, and by integration of existing examples. We use a property of spiders' webs to give new results concerning functions with no unbounded Fatou components.

References in corpus (1)

• Iteration of meromorphic functions

Cited by in corpus (7)

• Maximally and non-maximally fast escaping points of transcendental entire functions
• The size and topology of quasi-Fatou components of quasiregular maps
• Hollow quasi-Fatou components of quasiregular maps
• Dynamical sets whose union with infinity is connected
• Fast escaping points of entire functions: a new regularity condition
• The escaping set in transcendental dynamics
• On slow escaping and non-escaping points of quasimeromorphic mappings