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Dimensions of the boundaries of self-similar sets. (English) Zbl 1054.28006
Summary: We introduce a finite boundary type condition on iterated function systems of contractive similitudes on \(\mathbb R^d\). Under this condition, we compute the Hausdorff dimension of the boundary of the attractor in terms of the spectral radius of some finite off-spring matrix. We describe how to construct such a matrix. We also show that, in this case, the box dimension equals the Hausdorff dimension. In particular, this allows us to compute the Hausdorff dimension of the boundary of a class of self-similar sets defined by expansion matrices with noninteger entries.

MSC:
28A80 Fractals
28A78 Hausdorff and packing measures
37C45 Dimension theory of smooth dynamical systems
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