Speaker
Description
Thanks to the work of Aaronson, Doering and Mañé, Craizer, and many others, we know that the properties of an inner function and its dynamics in the unit disc are closely related to the dynamics of its boundary extension. If, however, we consider compositions of inner functions, i.e. non-autonomous dynamics in the unit disc, less is known about its relation to the corresponding non-autonomous dynamical system on the unit circle given by composing the boundary extensions. In this talk, we will tackle this problem from the point of view of ergodic theory. We will discuss necessary and sufficient conditions for mixing and ergodicity, construct examples and counterexamples, and present some consequences of ergodicity. This is joint work with Artur Nicolau (UAB).