Exponential separation of analytic self-conformal sets on the real line
Balázs Bárány (Budapest Univ. Techno. and Economics, Hungria)

In a recent article, Rapaport showed that there is no dimension drop for exponentially separated analytic IFSs on the real line. We show that the set of exponentially separated IFSs in the space of analytic IFSs contains an open and dense set in the C2 topology. Moreover, we give sucient conditions for the IFS to be exponentially separated, allowing us to construct explicit exponentially separated examples. The key technical tool is the introduction of the dual IFS, which we believe has signicant interest in its own right. As an application, we also characterise when an analytic IFS can be conjugated to a self-similar IFS. This is a joint work with Kolossváry and Troscheit.