Abstract

In this paper, we will consider subfractals, defined as a subset of the attractor of hyperbolic iterated function systems, which satisfy the open set condition. The subfractals will consist of points associated with infinite strings from a sofic subshift on the symbolic space. We find that the zeros of the lower and upper topological pressure functions are lower and upper bounds, respectively, for the Hausdorff, packing, lower and upper box dimensions of the subfractal.

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