# Dimension drop of connected part Of slicing self-affine Sponges

@article{Zhang2021DimensionDO,
title={Dimension drop of connected part Of slicing self-affine Sponges},
author={YAN-FANG Zhang and Yansong Xu},
journal={Journal of Mathematical Analysis and Applications},
year={2021}
}
• Published 19 October 2021
• Mathematics
• Journal of Mathematical Analysis and Applications
2 Citations

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## References

SHOWING 1-10 OF 30 REFERENCES
The Hausdorff and dynamical dimensions of self-affine sponges: a dimension gap result
• Mathematics
Inventiones 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
• Mathematics
Journal 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
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
• Mathematics
Journal 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
• Mathematics
Ergodic 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