## K. Igudesman

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

## (Lobachevskii Journal of Mathematics, Vol.12, pp.41-50)

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.

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