HAUSDORFF DIMENSIONS OF SOFIC AFFINE-INVARIANT SETS

Authors
KENYON R PERES Y
Citation
R. Kenyon et Y. Peres, HAUSDORFF DIMENSIONS OF SOFIC AFFINE-INVARIANT SETS, Israel Journal of Mathematics, 94, 1996, pp. 157-178
Citations number
31
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Israel Journal of Mathematics → ACNP
ISSN journal
00212172
Volume
94
Year of publication
1996
Pages
157 - 178
Database
ISI
SICI code
0021-2172(1996)94:<157:HDOSAS>2.0.ZU;2-Q
Abstract
We determine the Hausdorff and Minkowski dimensions of compact subsets of the 2-torus which are invariant under a linear endomorphism with i nteger eigenvalues and correspond to shifts of finite type or sofic sh ifts via some Markov partition. This extends a result of McMullen (198 4) and Bedford (1984), who considered full-shifts.