The series of papers [1-6] contains results obtianed in 1985-1988 in
collaboration with Sasha Blokh (with final touches put later in [7]).

They were largely motivated by * Milnor's Problem on
Attractors.*

Papers [4-5] prove * real a priori bounds * for infinitely renormalizable maps.

They were indepedently established by Dennis Sullivan
as the first step towards the * Feigenbaum-Coullet-Tresser Renormalization Conjecture.*

[The doubling case had been earlier handled by Guckenheimer.]