Geometry Working Seminar

Anthony McCormick, Pure Math Department, University of Waterloo

“Iterated Function Systems with Overlap”

In general, computing the Hausdorff dimension of a compact subset of Rn is very difficult. We will discuss the much more computationally feasible case in which our compact set arises from an iterated function system. Specifically, I will demonstrate a link between the weak sep- aration condition and roots of polynomials with coefficients in {0, 1, −1}. Then I will provide an outline of a systematic construction by Deng, Harding and Hu in which they transform iterated function systems with overlap into infinite iterated function systems satisfying the open set condition.

M3 2134