 Period-doubling renormalization operator

For a normalized even unimodal interval map with $f(0)=1$ and $a=f(1)\in (-1,0)$, defineThis returns the second iterate near the critical point to the original spatial and height normalization. Then $\mathcal{T}(f)(0)=f(1)/a=1$. A restrictive-interval condition is also needed for the composition to remain unimodal and map $[-1,1]$ into itself; normalization alone is not sufficient.

// Target: dynamical-systems.bigb