Balazs Barany, BME Budapest

Title:
Super-exponential condensation without exact overlaps

Abstract:
In the dimension theory of self-similar sets and measures, one of the important conjectures is the exact overlap conjecture. The conjecture says if the similarity dimension is strictly larger than the Hausdorff then there is an exact overlap between the functions of the corresponding IFS. The known strongest result in this direction is due to Hochman, who showed that exponential separation suffices for the equality of the Hausdorff and similitude dimensions of self-similar sets and measures. In this talk, we exhibit self-similar sets on the line which are not exponentially separated but do not generate any exact overlaps. This is a joint work with Antti Kaenmaki.