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.