In this project the principal investigator will study iterated function systems (IFS's) and subdivision algorithms (SDA's) in the context of dyadic iteration schemes governed by certain functional equations. The method of attack will involve analytical and numerical techniques that are based upon wavelet theory. The overall research plan has points of contact with the work on fractal geometry that is being conducted currently at Georgia Tech. In particular, the principal investigator will look at the following three interrelated aspects of solutions of functional equations: dimension and smoothness, the singularity spectrum and the inverse problem. The analysis of the geometry of sets of fractal dimension involves a number of different areas of mathematics, and it is safe to say that this subject has breathed new life into several parts of classical analysis. In this project the principal investigator will apply techniques from the theory of wavelets to study the properties of solution sets of functional equations whose graphs are fractals. Her approach will combine analytical and numerical methods, and she will be collaborating with the leading people in this work that blends analysis with geometry.
