منابع مشابه
Overlapping Self-affine Sets
We study families of possibly overlapping self-affine sets. Our main example is a family that can be considered the self-affine version of Bernoulli convolutions and was studied, in the non-overlapping case, by F. Przytycki and M. Urbański [23]. We extend their results to the overlapping region and also consider some extensions and generalizations.
متن کاملOverlapping Self-affine Sets of Kakeya Type
We compute the Minkowski dimension for a family of self-affine sets on R. Our result holds for every (rather than generic) set in the class. Moreover, we exhibit explicit open subsets of this class where we allow overlapping, and do not impose any conditions on the norms of the linear maps. The family under consideration was inspired by the theory of Kakeya sets.
متن کاملO ct 2 00 7 OVERLAPPING SELF - AFFINE SETS OF KAKEYA TYPE
We compute the Minkowski dimension for a family of self-affine sets on R. Our result holds for every (rather than generic) set in the class. Moreover, we exhibit explicit open subsets of this class where we allow overlapping, and do not impose any conditions on the norms of the linear maps. The family under consideration was inspired by the theory of Kakeya sets.
متن کاملSelf-Affine Sets with Positive Lebesgue Measure
Using techniques introduced by C. Güntürk, we prove that the attractors of a family of overlapping self-affine iterated function systems contain a neighbourhood of zero for all parameters in a certain range. This corresponds to giving conditions under which a single sequence may serve as a ‘simultaneous β-expansion’ of different numbers in different bases.
متن کاملCountable Alphabet Non-autnomous Self-affine Sets
We extend Falconer’s formula from [1] by identifying the Hausdorff dimension of the limit sets of almost all contracting affine iterated function systems to the case of an infinite alphabet, non-autonomous choice of iterating matrices, and time dependent random choice of translations.
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2006
ISSN: 0022-2518
DOI: 10.1512/iumj.2006.55.2718