Beijing Institute of Mathematical Sciences and Applications

Fractals are highly nonsmooth sets that often possess self-similarity, infinite irregularity, and non-integral Hausdorff dimension. They arise naturally in many branches of mathematics, science, and engineering. This is an introductory course on fractals. Topics include Hausdorff measure and dimension, box dimension, iterated function systems, self-similar sets, the collage theorem, the Moran-Hutchinson theorem, self-similar measures, and the multifractal formalism. Finally, a survey on iterated function systems with overlaps will be given; tentatively, topics will be selected from the weak separation property, the finite type condition, infinite Bernoulli convolutions and related results by Solomyak, Hochman, Varju, and others.