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 …

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 …

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 …

Lq-spectra of graph-directed planar non-conformal measures Page 1 Nonlinearity PAPER
Lq-spectra of graph-directed planar non-conformal measures To cite this article: Hua Qiu et al …

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 …

We compute the Hausdorff dimension of any random statistically self-affine Sierpinski
sponge K⊂ R k (k≥ 2) obtained by using some percolation process in [0, 1] k. To do so, we …

We present a self-contained proof of a formula for the L^ q dimensions of self-similar
measures on the real line under exponential separation (up to the proof of an inverse …

In this paper, we study the dimension theory of a class of piecewise affine systems in
euclidean spaces suggested by Michael Barnsley, with some applications to the fractal …

La géométrie fractale, qui entretient des liens étroits avec la théorie ergodique et la théorie
des probabilités, est un sujet très dynamique à l'échelle internationale. Un grand intérêt se …