The Geometry of Fractal Percolation and Randomly Perturbed Self-Affine Sets
In this short course we consider the geometric Measure theoretical properties of two families of random fractals: the Fractal percolation sets and the randomly perturbed self-affine sets.
Lectures 1-6: We study Fractal percolation sets from the point of their Hausdorff dimension, connectivity, existence of interval in projections, dimension of slices and rectifiability.
Lectures 7-10. We introduce the self-affine transversality condition for randomly perturbed self-affine sets. We extend this method to dominated triangular C1 mappings. Finally, we study the existence of interior points in randomly perturbed self-similar sets.