Logistic Map:
x_{n+1} = r · x_n · (1 − x_n)
Period doublings occur at r₁=3, r₂=3.449, r₃=3.544, r₄=3.5644…
Ratio δ=(r_n−r_{n-1})/(r_{n+1}−r_n) →
4.6692… (Feigenbaum const), universal across all unimodal maps (renormalization group).
Lyapunov λ>0 ⟺ chaos.