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

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.