# Lacunary self-similar fractal sets and intersection of Cantor sets

## (*Lobachevskii Journal of Mathematics, Volume XII*)

The problem on intersection of Cantor sets was examined in many papers. To solve this problem, we introduce the notion of lacunary self-similar set. The main difference to the standard (Hutchinson) notion of self-similarity is that the set of similarities used in the construction may vary from step to step in a certain way. We find the Hausdorff dimension of a lacunary self-similar set.