Rigorous verification of period-doubling bifurcations in maps

We present a computer-assisted approach for proving period-doubling bifurcations in one-parameter families of maps $x \mapsto f(x,λ)$ on $\mathbb{R}^n$. We solve a square augmented system, called the period-doubling map, whose unknowns are the fixed point, the parameter, the right eigenvector attach