Geodesic
A certain family of self-similar sets
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2011), pp. 31-45

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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
Mots-clés : Hausdorff dimension. 
@article{IVM_2011_2_a3,
     author = {K. B. Igudesman},
     title = {A certain family of self-similar sets},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {31--45},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_2_a3/}
}
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K. B. Igudesman. A certain family of self-similar sets. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2011), pp. 31-45. http://geodesic.mathdoc.fr/item/IVM_2011_2_a3/