Based on the work of Mauldin and Williams ['On the Hausdorff dimension of some graphs',
Trans. Amer. Math. Soc. 298 (2)(1986), 793–803] on convex Lipschitz functions, we prove …

Let {S i} i∈ Λ be a finite contracting affine iterated function system (IFS) on R d. Let (Σ, σ)
denote the two-sided full shift over the alphabet Λ, and let π: Σ→ R d be the coding map …

Under mild conditions we show that the affinity dimension of a planar self-affine set is equal
to the supremum of the Lyapunov dimensions of self-affine measures supported on self …

Let $\Phi:=\left\{(x_ {1},..., x_ {d})\rightarrow\left (r_ {i, 1} x_ {1}+ a_ {i, 1},..., r_ {i, d} x_ {d}+ a_
{i, d}\right)\right\} _ {i\in\Lambda} $ be an affine diagonal IFS on $\mathbb {R}^{d} $. Suppose …

In this paper, a sponge in R d R^d is the attractor of an iterated function system consisting of
finitely many strictly contracting affine maps whose linear part is a diagonal matrix. A suitable …

arxiv:1703.08564v1 [math.DS] 24 Mar 2017 Page 1 SHRINKING TARGETS ON BEDFORD-MCMULLEN
CARPETS BALÁZS BÁRÁNY AND MICHA L RAMS Abstract. We describe the shrinking target …

We construct a family of planar self-affine carpets with overlaps using lower triangular
matrices in a way that generalizes the original Gatzouras–Lalley carpets (Gatzouras and …

As a continuation of a recent work [Bárány et al, On the dimension of self-affine sets and
measures with overlaps. Proc. Amer. Math. Soc. 144 (2016) 4427–4440] of the same …

In this paper we consider iterated function systems (IFS) on the real line consisting of
continuous piecewise linear functions. We assume some bounds on the contraction ratios of …

Let $\mu $ be a self-affine measure associated with a diagonal affine iterated function
system (IFS) $\Phi=\{(x_ {1},\ldots, x_ {d})\mapsto (r_ {i, 1} x_ {1}+ t_ {i, 1},\ldots, r_ {i, d} x …