This article is cited in 2 papers

A certain family of self-similar sets

K. B. Igudesman

Chair of Geometry, Kazan State University, Kazan, Russia

Abstract: In this paper we consider an one-parameter family of iterated function systems. For every value of the parameter we find the set of top addresses. We prove that this set is a countable disjoint union of self-similar sets and calculate its Hausdorff dimension.

Keywords: iterated function systems, attractor, top address, self-similarity, Hausdorff dimension.

UDC: 517.987+511.72

Received: 16.06.2009

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:2, 26–38

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