Dimension of generic self-affine sets with holes
نویسندگان
چکیده
منابع مشابه
Genericity of Dimension Drop on Self-affine Sets
We prove that generically, for a self-affine set in R, removing one of the affine maps which defines the set results in a strict reduction of the Hausdorff dimension. This gives a partial positive answer to a folklore open question.
متن کاملOverlapping 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 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 کاملAssouad Dimension of Self-affine Carpets
We calculate the Assouad dimension of the self-affine carpets of Bedford and McMullen, and of Lalley and Gatzouras. We also calculate the conformal Assouad dimension of those carpets that are not self-similar.
متن کاملExplicit Bounds for the Hausdorff Dimension of Certain Self-Affine Sets
A lower bound of the Hausdorff dimension of certain self-affine sets is given. Moreover, this and other known bounds such as the box dimension are expressed in terms of solutions of simple equations involving the singular values of the affinities. Keyword Codes: G.2.1;G.3
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2018
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-018-1187-6