Global convergence of the second order Ricker equation

We present a short analytic proof of a 1976 conjecture on the global dynamics of the equation xn=xn−1ex−xn−2xn=xn−1ex−xn−2, where x∈(0,1)x∈(0,1) and x0,x1∈(0,+∞)x0,x1∈(0,+∞). The proof is based on considering the parameter xx in the previous equation as a complex variable. This transforms the problem in studying the asymptotic behaviour of a sequence of analytic functions.