Perturbations of slowly recurrent Collet-Eckmann maps
Two Dimensional Maps
26 January 15:00 - 16:00
Magnus Aspenberg - Lund University
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.
KTH Royal Institute of Technology
The University of Cergy-Pontoise
University of Exeter