Abstract:
In this talk we will give an overview of iterated function systems and their generalization to non-autonomous and graph directed systems, as well as techniques to calculate the Hausdorff dimension of their limit sets. In 1979 Rufus Bowen was able to show that the Hausdorff dimension of a quasi circle is equal to the unique zero of the pressure function. We will discuss Bowen's formula as it relates to each generalization of iterated function systems and give a proof of Bowen's formula for a class of non-autonomous graph directed Markov systems.