Amlan Banaji

Dimensions of infinitely generated self-conformal sets

Many fractals can be realised as the limit set of an iterated function system (IFS) of contracting maps. If the IFS consists of a countably infinite number of maps, then different notions of fractal dimension of the resulting limit set, such as Hausdorff, box and Assouad-type dimensions, can take different values, even if the contractions are assumed to be conformal and well-separated. We will explain what is known about these dimensions in this setting, and describe applications to parabolic Cantor sets, and to sets of numbers which have continued fraction expansions with restricted entries. This talk is based on joint work with Jonathan Fraser.