7 maj 2007, kl 13.15-14.15, Uppsala, Ångström, sal 64119.

Thomas Jordan (University of Warwick): The dimension of randomly perturbed self-affine sets

Abstract. The Hausdorff dimension of self-similar sets satisfying the open set condition is well known. However in the self-affine case the situation, even with the open set condition, is much more complicated. The Hausdorff dimension is not necessarily continuous with parameters for the self-affine set. Over 15 years ago Falconer calculated a formula for the Hausdorff dimension of self-affine sets which holds generically (I will make it clear what this means) assuming the norms of the matrices are smaller than 1/2. We will look at the case of adding random errors to the iterated function system. In this case for suitably chosen random errors Falconer's formula holds almost surely with no assumption on the norm.