Shrinking targets on Bedford-McMullen carpets

Multifractal Analysis for Bedford-mcmullen Carpets

In this paper we compute the multifractal analysis for local dimensions of Bernoulli measures supported on the self-affine carpets introduced by Bedford-McMullen. This extends the work of King where the multifractal analysis is computed with strong additional separation assumptions.

A random version of McMullen–Bedford general Sierpinski carpets and its application

We consider a random version of the McMullen–Bedford general Sierpinski carpet which is constructed by randomly choosing patterns in each step instead of a single pattern in its original form. Their Hausdorff, packing and box-counting dimensions are determined. A sufficient condition and a necessary condition for the Hausdorff measures in their dimensions to be positive are given. As an applica...

Assouad 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.

ON SHRINKING TARGETS FOR Zm ACTIONS ON TORI

Let A be an n × m matrix with real entries. Consider the set BadA of x ∈ [0, 1)n for which there exists a constant c(x) > 0 such that for any q ∈ Zm the distance between x and the point {Aq} is at least c(x)|q|−m/n . It is shown that the intersection of BadA with any suitably regular fractal set is of maximal Hausdorff dimension. The linear form systems investigated in this paper are natural ex...

Shrinking Targets for Regularization of Logistic Regression