Notes on the Transversality Method for Iterated Function Systems—A Survey

Abstract

This is a brief survey of selected results obtained using the “transversality method” developed for studying parametrized families of fractal sets and measures. We mostly focus on the early development of the theory, restricting ourselves to self-similar and self-conformal iterated function systems.

Typical absolute continuity for classes of dynamically defined measures

“…In fact, claim (1) can be seen in the same way for the Hausdorff dimension, as hµ χµ(F λ ) = dim H (µ, d λ ). See [18] for a recent survey on transversality methods for IFS's, which elaborates on the connections between Theorem 1.14 and Marstrand-Mattila projection theorems for orthogonal projections.…”