We 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.
Publié le : 2003-05-14
Classification:
Self-similar set,
self-similar tile,
self-affine tile,
finite type condition,
finite boundary type condition,
Hausdorff dimension,
box dimension,
28A78,
28A80
@article{1064858781,
author = {Lau, Ka-Sing and Ngai, Sze-Man},
title = {Dimensions of the Boundaries of Self-Similar Sets},
journal = {Experiment. Math.},
volume = {12},
number = {1},
year = {2003},
pages = { 13-26},
language = {en},
url = {http://dml.mathdoc.fr/item/1064858781}
}
Lau, Ka-Sing; Ngai, Sze-Man. Dimensions of the Boundaries of Self-Similar Sets. Experiment. Math., Tome 12 (2003) no. 1, pp. 13-26. http://gdmltest.u-ga.fr/item/1064858781/