Random logistic maps and Lyapunov exponents (Q1866446)

The author studies iterates logistic maps with random i.i.d. parameters. He shows that when the Lyapunov exponent is negative the iterates converge to a random point, called a random point attractor, which is independent of the initial point. The distribution of this random point is the invariant measure of the corresponding Markov chain. If the Lyapunov exponent is positive such convergence does not take place.