A Computer-Assisted Proof of the Feigenbaum Conjectures

Let M denote the space of continuously differential)le even mappings φ of the interval [-1, 1] into itself such that

Ml. ψ(0)= 1,

M2. χφ'(χ)<0 for χ Φ 0. M2 says that φ is strictly increasing on [-1, 0) and strictly decreasing on (0, 1], so M is a space of mappings which are unimodal in a strict sense.