Average measure-theoretic entropy for a family of expanding on average random Blaschke products

Abstract

This work gives a computable formula for the average measure-theoretic entropy of a family of expanding on average random Blaschke products, generalizing the paper by Pujals, Robert and Shub [Expanding maps of the circle rerevisited: positive Lyapunov exponents in a rich family. Ergod. Th. & Dynam. Sys. 26 (6) (2006), 1931–1937] to the random setting. In doing so, we describe the random invariant measure and associated measure-theoretic entropy for a class of admissible random Blaschke products, allowing for maps which are not necessarily expanding and may even have an attracting fixed point.