Invariant densities for random maps of the interval

Source abstract

A random map is a discrete time process in which one of a number of functions is selected at random and applied. Here we study random maps of [ 0 , 1 ] [0,1] which represent dynamical systems on the square [ 0 , 1 ] × [ 0 , 1 ] [0,1] \times [0,1] . Sufficient conditions for a random map to have an absolutely continuous invariant measure are given, and the number of ergodic components of a random map is discussed.