Dimension Functions of Self-Affine Scaling Sets Academic Article uri icon

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abstract

  • Abstract.In this paper, the dimension function of a self-affine generalized scaling set associated with an n×n integral expansive dilation A is studied. More specifically, we consider the dimension function of an A-dilation generalized scaling set K assuming that K is a self-affine tile satisfying BK = (K+d1)[ (K + d2), where B = At , A is an n×n integral expansive matrix with |det A| = 2, and d1, d2 ∊ ℝn. We show that the dimension function of K must be constant if either n = 1 or 2 or one of the digits is 0, and that it is bounded by 2|K| for any n.

publication date

  • December 1, 2013