Falconer’s Formula for the Hausdorff Dimension of a Self–Affine Set in R

نویسندگان

  • Irene Hueter
  • Steven P. Lalley
چکیده

Simple sufficient conditions are given for the validity of a formula of Falconer [3] describing the Hausdorff dimension of a self-affine set. These conditions are natural (and easily checked) geometric restrictions on the actions of the affine mappings determining the self-affine set. It is also shown that under these hypotheses the self-affine set supports an invariant Gibbs measure whose Hausdorff dimension equals that of the set.

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تاریخ انتشار 1995