## One Citation

Relations between topological and metrical properties of self-affine Sierpi$\acute{\text{n}}$ski sponges

- Mathematics
- 2020

We investigate two Lipschitz invariants of metric spaces defined by δ-connected components, called the maximal power law property and the perfectly disconnectedness. The first property has been…

## References

SHOWING 1-10 OF 30 REFERENCES

The Hausdorff and dynamical dimensions of self-affine sponges: a dimension gap result

- Mathematics, MedicineInventiones mathematicae
- 2017

A self-affine sponge is constructed in R3 whose dynamical dimension is strictly less than its Hausdorff dimension, resolving a long-standing open problem in the dimension theory of dynamical systems, namely whether every expanding repeller has an ergodic invariant measure of full Hausdorf dimension.

Hausdorff dimension in graph directed constructions

- Mathematics
- 1988

We introduce the notion of geometric constructions in Rm governed by a directed graph G and by similarity ratios which are labelled with the edges of this graph. For each such construction, we…

Structure of equilibrium states on self‐affine sets and strict monotonicity of affinity dimension

- Mathematics
- 2016

A fundamental problem in the dimension theory of self-affine sets is the construction of high-
dimensional measures which yield sharp lower bounds for the Hausdorff dimension of the set.
A natural…

Crinkly curves, Markov partitions and dimension

- Mathematics
- 1984

We consider the relationship between fractals and
dynamical systems. In particular we look at how the
construction of fractals in (D1) can be interpreted-in a
dynamical setting and additionally…

Gap sequences of fractal cubes and Bedford-McMullen carpets

- Mathematics
- 2020

Gap sequence describes the number of $\delta$-connected components of a compact set, it is used in mathematics for many different purposes. We say a compact set $E$ is almost discrete, if its gap…

A Class of Self-Affine Sets and Self-Affine Measures

- Mathematics
- 2005

Let I = {φj}j=1 be an iterated function system (IFS) consisting of a family of contractive affine maps on Rd. Hutchinson [13] proved that there exists a unique compact setK = K(I), called the…

Hausdorff dimension of the limit sets of some planar geometric constructions

- Mathematics
- 2007

Abstract We determine the Hausdorff and box dimension of the limit sets for some class of planar non-Moran-like geometric constructions generalizing the Bedford–McMullen general Sierpinski carpets.…

Gibbs measures on self-affine Sierpiński carpets and their singularity spectrum

- MathematicsErgodic Theory and Dynamical Systems
- 2007

Abstract We consider a class of Gibbs measures on self-affine Sierpiński carpets and perform the multifractal analysis of its elements. These deterministic measures are Gibbs measures associated with…