Fast basins, fractal manifolds, and flows on attractors of iterated function systems (IFSs)

Since their introduction, thirty years ago, IFSs have become a widely used concept. Reasons for this success include the simplicity of the IFSs themselves and the richness of their attractors. This talk will define, characterize, and exemplify, a number of new basic structures that arise naturally from an attractor of an IFS. The driving force behind these structures is a direct generalization of the notion of analytic continuation from smooth to rough.