Weiwei Cui: Speiser meets Misiurewicz

Abstract:

We propose a Misiurewicz condition for transcendental entire functions and study perturbations of Misiurewicz functions in their natural parameter spaces. We show that Misiurewicz functions can be approximated by hyperbolic functions. However, they are rare in the parameter space in the sense that the set of such maps has Lebesgue measure zero. This is based on a joint work with Magnus Aspenberg.