Israel Journal of Mathematics

, Volume 94, Issue 1, pp 157–178 | Cite as

Hausdorff dimensions of sofic affine-invariant sets

  • R. Kenyon
  • Y. Peres


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.


Spectral Radius Hausdorff Dimension Finite Type Topological Entropy Sierpinski Gasket 
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Copyright information

© The Magnes Press 1996

Authors and Affiliations

  • R. Kenyon
    • 1
  • Y. Peres
    • 2
  1. 1.CNRS UMR 128Ecole Normale Supérieure de LyonLyonFrance
  2. 2.Department of StatisticsUniversity of California at BerkeleyBerkeleyUSA

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