Dimensions of the boundaries of self-similar sets
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AbstractWe introduce a finite boundary type condition on iterated function systems of contractive similitudes on R-d. Under this condition, we compute the Hausdorff dimension of the boundary of the attractor in terms of the spectral radius of some finite offspring matrix. We describe how to construct such a matrix. We also show that, in this case, the box dimension equals the Hausdorff dimension in particular, this allows us to compute the Hausdorff dimension of the boundary of a class of self-similar sets defined by expansion matrices with noninteger entries.
All Author(s) ListLau KS, Ngai SM
Journal nameExperimental Mathematics
Volume Number12
Issue Number1
Pages13 - 26
LanguagesEnglish-United Kingdom
Keywordsbox dimension; finite boundary type condition; finite type condition; Hausdorff dimension; self-affine tile; self-similar set; self-similar tile
Web of Science Subject CategoriesMathematics; MATHEMATICS

Last updated on 2021-11-09 at 23:45