Dynamics of Probability Measures: Affine Representation and other Aspects

I will discuss the concept of affine representation for topological dynamical systems. This leads naturally to the study of dynamics induced onto the space of probability measures. Some qualitative relationships between a dynamical system and its lifting to the probability space are shown. I will also give a differentiable approach to dynamics on the space of probability measures. This structure implies that notions from differentiable dynamics may be carried over to the representation of a system that has no differentiable structure itself.