The Assouad dimension is a notion of dimension in fractal geometry that has been the
subject of much interest in recent years. This book, written by a world expert on the topic, is …

Let X= ⋃ φ _ i XX=⋃ φ i X be a strongly separated self-affine set in R^ 2 R 2 (or one
satisfying the strong open set condition). Under mild non-conformality and irreducibility …

We prove that if is a self-affine measure in the plane whose defining IFS acts totally
irreducibly on RP 1 and satisfies an exponential separation condition, then its dimension is …

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 …

In this paper, we solve the long standing open problem on exact dimensionality of self-affine
measures on the plane. We show that every self-affine measure on the plane is exact …

Let μ μ be a measure on SL _ 2 (R) SL 2 (R) generating a non-compact and totally
irreducible subgroup, and let ν ν be the associated stationary (Furstenberg) measure for the …

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 …

Suppose F is a self-affine set on R d, d≥ 2, which is not a singleton, associated to affine
contractions fj= A j+ bj, A j∈ GL (d, R), bj∈ R d, j∈ A, for some finite A. We prove that if the …

Ledrappier and Young introduced a relation between entropy, Lyapunov exponents and
dimension for invariant measures of diffeomorphisms on compact manifolds. In this paper …

We completely describe the equilibrium states of a class of potentials over the full shift which
includes Falconer's singular value function for affine iterated function systems with invertible …