Abstract
AbstractWe study the Hausdorff dimension and measures of full Hausdorff dimension for a compact invariant set of an expanding non-conformal map on the torus given by an integer-valued diagonal matrix. The Hausdorff dimension of a ‘general Sierpiński carpet’ was found by McMullen and Bedford and the uniqueness of the measure of full Hausdorff dimension in some cases was proved by Kenyon and Peres. We extend these results by using compensation functions to study a general Sierpiński carpet represented by a shift of finite type. We give some conditions under which a general Sierpiński carpet has a unique measure of full Hausdorff dimension and study the properties of the unique measure.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
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