Random conformal dynamical systems (Q2475581)

Random compositions of elements of a pseudogroup acting conformally on a manifold are studied. The following dichotomy (in case that probabilities are symmetric) is shown: either there is a probability measure preserved by all elements of the pseudogroup supported on a minimal subset or the system has the property of exponential contraction: for any point and almost every random composition of elements of the pseudogroup there is a neighborhood of the point which is contracted exponentially.