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