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Fractals and Number Systems in Real Quadratic Number Fields

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Abstract

In this paper we compute the box counting dimension of sets, that are related to number systems in real quadratic number fields. The sets under discussion are so-called graph-directed self affine sets. Contrary to the case of self similar sets, for self affine sets there does not exist a general theory for the determination of the box counting dimension. Thus we are forced to construct the covers, needed for its calculation, directly.

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  1. INSTITUT FÜR MATHEMATIK UND ANGEWANDTE GEOMETRIE, ABTEILUNG FÜR MATHEMATIK UND STATISTIK, MONTANUNIVERSITÄT LEOBEN, FRANZ-JOSEF-STRAßE 18, A-8700, LEOBEN, AUSTRIA

    J. M. Thuswaldner

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  1. J. M. Thuswaldner
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Thuswaldner, J.M. Fractals and Number Systems in Real Quadratic Number Fields. Acta Mathematica Hungarica 90, 253–269 (2001). https://doi.org/10.1023/A:1006710730004

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  • DOI: https://doi.org/10.1023/A:1006710730004

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