On a family of self-affine sets: Topology, uniqueness, simultaneous expansions Page 1 Ergod.
Th. & Dynam. Sys. (2017), 37, 193–227 doi:10.1017/etds.2015.41 c Cambridge University …

Let $ T_1,\ldots, T_m $ be a family of $ d\times d $ invertible real matrices with $\| T_i\|< 1/2$
for $1\leq i\leq m $. We provide some sufficient conditions on these matrices such that the …

Let M be a $2\times 2$ real matrix with both eigenvalues less than 1 in modulus. Consider
two self-affine contraction maps from ${{\mathbb {R}}^{2}}\to {{\mathbb {R}}^{2}} $, Tm (v) …

In this paper we study digit frequencies in the setting of expansions in non-integer bases,
and self-affine sets with non-empty interior. Within expansions in non-integer bases we …

We prove that for random affine code tree fractals the affinity dimension is almost surely
equal to the unique zero of the pressure function. As a consequence, we show that the …

We investigate the existence of simultaneous representations of real numbers x in bases 1<
q 1<…< qr, r≥ 2, with a finite digit set A⊂ ℝ. We prove that if A contains both positive and …

In this paper we study the set of digit frequencies that are realised by elements of the set of β
β-expansions. The main result of this paper demonstrates that as β β approaches 1, the set …

Let $ C $ be the middle-third Cantor set, and $ f $ a continuous function defined on an open
set $ U\subset\mathbb {R}^{2} $. Denote the image\begin {equation*} f_ {U}(C, C)=\{f (x, y):(x …

Let K be the attractor of the following iterated function system (IFS){f 1 (x)= λ x, f 2 (x)= λ x+ c−
λ, f 3 (x)= λ x+ 1− λ}, where f 1 (I)∩ f 2 (I)≠∅,(f 1 (I)∪ f 2 (I))∩ f 3 (I)=∅, and I=[0, 1] is the …

Let $ M $ be a $ d\times d $ contracting matrix. In this paper we consider the self-affine
iterated function system $\{Mv-u, Mv+ u\} $, where $ u $ is a cyclic vector. Our main result is …