## 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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Verfasserangaben: Peter Mörters, Daniela Krieg urn:nbn:de:hbz:386-kluedo-7880 Preprints (rote Reihe) des Fachbereich Mathematik (293) Preprint Englisch 1996 1996 Technische Universität Kaiserslautern 03.04.2000 Cantor sets ; fractals ; limit models; tangent measure distributions Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 510 Mathematik 28-XX MEASURE AND INTEGRATION (For analysis on manifolds, see 58-XX) / 28Axx Classical measure theory / 28A75 Length, area, volume, other geometric measure theory [See also 26B15, 49Q15] 28-XX MEASURE AND INTEGRATION (For analysis on manifolds, see 58-XX) / 28Axx Classical measure theory / 28A80 Fractals [See also 37Fxx] Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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