相关论文: Assouad and quasi-Assouad dimensions of Moran sets
We obtain the Assouad dimensions of Moran sets under suitable condition. Using the homogeneous set, we also study the Assouad dimensions of Cantor-like sets.
In analogy with the lower Assouad dimensions of a set, we study the lower Assouad dimensions of a measure. As with the upper Assouad dimensions, the lower Assouad dimensions of a measure provide information about the extreme local behaviour…
In this paper, we give the Assouad dimension formula and the upper bound of the lower dimension for homogeneous Moran sets under the condition $\sup_{k\ge 1}\{n_{k}\}<+\infty$. We also give the Assouad spectrum and the lower spectrum…
In this paper we study the range of possible almost sure dimensions of random measures arising from a natural model of random Moran measures. Specifically, we consider the Assouad-like ``large'' $\Phi$-dimensions of these measures. These…
In this paper, we determine the almost sure values of the $\Phi $-dimensions of random measures supported on random Moran sets that satisfy a uniform separation condition. The $\Phi $-dimensions are intermediate Assouad-like dimensions, the…
The Assouad and quasi-Assouad dimensions of a metric space provide information about the extreme local geometric nature of the set. The Assouad dimension of a set has a measure theoretic analogue, which is also known as the upper regularity…
Intermediate dimensions are a class of new fractal dimensions which provide a spectrum of dimensions interpolating between the Hausdorff and box-counting dimensions. In this paper, we study the intermediate dimensions of Moran sets. Moran…
In this paper, we study the quasisymmetric Hausdorff minimality of homogeneous Moran sets. First, we obtain the Hausdorff dimension formula of two classes of homogeneous Moran sets which satisfy some conditions. Second, we show two special…
We study the Assouad and quasi-Assoaud dimensions of dominated rectangular self-affine sets in the plane. In contrast to previous work on the dimension theory of self-affine sets, we assume that the sets satisfy certain separation…
In this paper we study the Assouad-like $\Phi$ dimensions of sets and measures that are constructed by a random weighted iterated function system of similarities. These dimensions are distinguished by the depth of the scales considered and…
In this paper, we determine the almost sure values of the $\Phi$-dimensions of random measures $\mu$ supported on random Moran sets in $\R^d$ that satisfy a uniform separation condition. This paper generalizes earlier work done on random…
The connections between quasi-Assouad dimension and tangents are studied. We apply these results to the calculation of the quasi-Assouad dimension for a class of planar self-affine sets. We also show that sets with decreasing gaps have…
Given a non-negative, decreasing sequence $a$ with sum $1$, we consider all the closed subsets of $[0,1]$ such that the lengths of their complementary open intervals are given by the terms of $a$, the so-called complementary sets. In this…
The upper and lower Assouad dimensions of a metric space are local variants of the box dimensions of the space and provide quantitative information about the `thickest' and `thinnest' parts of the set. Less extreme versions of these…
We investigate the distortion of the Assouad dimension and (regularized) spectrum of sets under planar quasiregular maps. While the respective results for the Hausdorff and upper box-counting dimension follow immediately from their…
The uniform disconnectedness is an important invariant property under bi-Lipschitz mapping, and the Assouad dimension $\dim _{A}X<1$ implies the uniform disconnectedness of $X$. According to quasi-Lipschitz mapping, we introduce the…
In this paper, we are concerned with the relationship among the lower Assouad type dimensions. For uniformly perfect sets in doubling metric spaces, we obtain a variational result between two different but closely related lower Assouad…
We study the dimension theory of limit sets of iterated function systems consisting of a countably infinite number of conformal contractions. Our focus is on the Assouad type dimensions, which give information about the local structure of…
We introduce a probability distribution on $\mathcal{P}([0,1]^d)$, the space of all Borel probability measures on $[0,1]^d$. Under this distribution, almost all measures are shown to have infinite upper quasi-Assouad dimension and zero…
The class of stochastically self-similar sets contains many famous examples of random sets, e.g. Mandelbrot percolation and general fractal percolation. Under the assumption of the uniform open set condition and some mild assumptions on the…