The Open University ’ s repository of research publications and other research outputs Connectedness properties of the set where the iterates of an entire function are bounded
نویسنده
چکیده
We investigate some connectedness properties of the set of points K(f) where the iterates of an entire function f are bounded. We describe a class of transcendental entire functions for which K(f) is totally disconnected if and only if each component of K(f) containing a critical point is aperiodic. Moreover we show that, for such functions, if K(f) is disconnected then it has uncountably many components. We give examples of functions for which K(f) is totally disconnected, and we use quasiconformal surgery to construct a function for which K(f) has a component with empty interior that is not a singleton.
منابع مشابه
research outputs Connectedness properties of the set where the iterates
We investigate some connectedness properties of the set of points K(f) where the iterates of an entire function f are bounded. We describe a class of transcendental entire functions for which K(f) is totally disconnected if and only if each component of K(f) containing a critical point is aperiodic. Moreover we show that, for such functions, if K(f) is disconnected then it has uncountably many ...
متن کاملConnectedness properties of the set where the iterates of an entire function are bounded
We investigate some connectedness properties of the set of points K(f) where the iterates of an entire function f are bounded. We describe a class of transcendental entire functions for which K(f) is totally disconnected if and only if each component of K(f) containing a critical point is aperiodic. Moreover we show that, for such functions, if K(f) is disconnected then it has uncountably many ...
متن کاملThe Open University ’ s repository of research publications and other research outputs 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 comp...
متن کاملThe Open University ’ s repository of research publications and other research outputs Entire functions for which the escaping set is a
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...
متن کاملThe Open University ’ s repository of research publications and other research outputs Creativity in the design process : co - evolution of prob
The Open University's repository of research publications and other research outputs Creativity in the design process: co-evolution of prob-lem–solution Journal Article
متن کامل