Tangent measure distributions of hyperbolic Cantor sets

  • Tangent measure distributions were introduced by Bandt and Graf as a means to describe the local geometry of self-similar sets generated by iteration of contractive similitudes. In this paper we study the tangent measure distributions of hyperbolic Cantor sets generated by contractive mappings, which are not similitudes. We show that the tangent measure distributions of these sets equipped with either Hausdorff or Gibbs measure are unique almost everywhere and give an explicit formula describing them as probability distributions on the set of limit models of Bedford and Fisher.

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Author:Peter Mörters, Daniela Krieg
URN (permanent link):urn:nbn:de:hbz:386-kluedo-7880
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (293)
Document Type:Preprint
Language of publication:English
Year of Completion:1996
Year of Publication:1996
Publishing Institute:Technische Universität Kaiserslautern
Tag:Cantor sets ; fractals ; limit models; tangent measure distributions
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):28A75 Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]
28A80 Fractals [See also 37Fxx]

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