## 2 Citations

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…

Relations between topological and metrical properties of self-affine Sierpiński sponges

- MathematicsJournal of Mathematical Analysis and Applications
- 2022

## References

SHOWING 1-10 OF 30 REFERENCES

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

- MathematicsInventiones 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.

A dimension drop phenomenon of fractal cubes

- MathematicsJournal of Mathematical Analysis and Applications
- 2020

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…

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…

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…

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

- MathematicsJournal of Fourier Analysis and Applications
- 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…

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…