## Institute for Mathematical Sciences

## Preprint ims97-1

** J.J.P. Veerman**
* Hausdorff Dimension of Boundaries of Self-Affine Tiles in R^n*

Abstract: We present a new method to calculate the Hausdorff dimension of a certain class of fractals: boundaries of self-affine tiles.
Among the interesting aspects are that even if the affine
contraction underlying the iterated function system is not
conjugated to a similarity we obtain an upper- and and
lower-bound for its Hausdorff dimension. In fact, we obtain the
exact value for the dimension if the moduli of the eigenvalues
of the underlying affine contraction are all equal (this
includes Jordan blocks). The tiles we discuss play an important
role in the theory of wavelets.
We calculate the dimension for a number of examples.

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