Invariant measures for random iterations of affine maps.
Abstract. We consider actions of the free semigroup with 2 generators on the real line. The generators act as affine maps, one contracting and one expanding, with distinct fixed points. Then every orbit is dense in a half-line, and we can ask whether it is, in some sense, uniformly distributed. We present answers to this question for various interpretations of the phrase "uniformly distributed". The results were obtained jointly with Vitaly Bergelson and Samuel Senti.