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Hausdorff dimensions of sofic affine-invariant sets

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Abstract

We determine the Hausdorff and Minkowski dimensions of compact subsets of the 2-torus which are invariant under a linear endomorphism with integer eigenvalues and correspond to shifts of finite type or sofic shifts via some Markov partition. This extends a result of McMullen (1984) and Bedford (1984), who considered full-shifts.

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Authors and Affiliations

  1. CNRS UMR 128, Ecole Normale Supérieure de Lyon, 46, allée d'Italie, 69364, Lyon, France

    R. Kenyon

  2. Department of Statistics, University of California at Berkeley, 94720, Berkeley, CA, USA

    Y. Peres

Authors
  1. R. Kenyon
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  2. Y. Peres
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Additional information

This work was completed while the first author was at the Institut Fourier, Grenoble, France, and at MSRI, Berkeley, CA. The research at MSRI was supported in part by NSF grant #DMS 9022140.

This work was completed while the second author was at Yale University. Received July 8, 1994

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Kenyon, R., Peres, Y. Hausdorff dimensions of sofic affine-invariant sets. Israel J. Math. 94, 157–178 (1996). https://doi.org/10.1007/BF02762702

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  • DOI: https://doi.org/10.1007/BF02762702

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