Joint with G. Levin

This is a part of our long-going project to study limits of conformal dynamical systems whose degree of criticality tends to infinity with the goal of finding or excluding examples of wild attractors and Julia sets of positive measure. The key construction is an induced Markov map and the quantity to calcaulate is its drift, both introduced in the work of Bruin et al. from 1994. The recent is that for Feigenbaum polynomials the drift has a finite limit. This is not particularly welcome news since the sign of the drift needs to be determined. The talk will explain the background of this result, main constructions and questions involved.