Magnus Aspenberg, Lund Univsity
Conjecturally, almost every rational map is either hyperbolic or non-uniformly expanding, i.e. satisfies the Collet-Eckmann condition (CE). In this talk I will present two results on perturbations of CE-maps, where the main novelty is to allow the critical set to be recurrent at a slow rate (slowly recurrent maps). Suppose f is such a slowly recurrent CE-map. If the Julia set is the whole sphere, then f is a Lebesgue density point of CE-maps, and if the Julia set is not the whole sphere, then f is a Lebesgue density point of hyperbolic maps.
The last part is a joint work with M. Bylund and W. Cui.