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