一类Moran测度的重分形谱

证明一类支撑在某些Moran分形上的Moran测度的重分形形式成立.     

一类Moran测度的Hentschel—Procaccia维数

本文研究了一类Moran测度.利用降阶补齐的方法,得出了一类Moran测度的Hentschel-Procaccia维数.     

一类齐次Moran集的Hausdorff测度

本文研究了一类新的齐次Moran集.利用x~s(0s1)的凸性方法,获得了它的Hausdorff测度,推广了齐次cantor集的结果.     

一类Moran测度的谱性

令R_k=(ak00bk)为正整数扩张矩阵,D_k={0,1,…,q_k-1}v_1+{0,1,…,q_k-1}v_2,其中v_1=(1,0)~t,v_2=(0,1)~t,q_k1为正整数.本文研究由{R_k}_(k=1)~∞和{D_}_(k=1)~∞生成的Moran测度μ{R_k},{D_k} :=δ_(R1)(-1)~D_1*δ(R_2R_1)~(-1)D_2*···*δ(R_K···R_2R_1)(-1)D_K*···的谱性,证明了当q_k|a_k且q_k|b_k时,μ{R_k},{D_k}为谱测度.这推广了文献[J.Funct,Anal.,2014,266(1):343-354]和[J.Funct.Anal.,2002,193(2):409-420]中的结论.     

广义Moran集上概率测度的多重分形分析

本文讨论了广义Moran集K上的概率测度的多重分形性质。采用更一般地办法定义函数f(。)来刻划K上概率测度的多重分形特征。此外,还讨论了信息维数的一些性质。     

Rn中一类具有N元数字集的自仿测度的谱性

假设R∈Mn(Z)为扩张矩阵和N元数字集D={0,a1,a2,…,aN-1}u三{0,1,…,N-1}u (modN),这里u∈Zn{0).该文主要研究由D和R生成的自仿测度μR,D的谱性,得到了μR,D为谱测度的一个充分条件.对于一些特殊情况,得到了μR,D为谱测度的一个充分必要条件,并给出其谱的具体表达式.     

一类广义齐次Moran集的Hausdorff维数

本文构造了一类具有类似高维Moran结构的集合,给出一些充分条件来计算其Hausdorff维数.     

一类SierPinski地毯的Hausdorff测度的初等证明

在平面上以直径为d(d>0)的正M边形为基本集(M≥3为整数),构造压缩比为1∶k(k为不小于M的实数)的广义Sierpinski地毯,并用初等方法计算出它的Hausdorff测度为ds,其中s=logkM.     

齐次均匀Moran集的拟Lipschitz等价

本文证明了两个正则齐次均匀Moran集拟Lipschitz等价当且仅当它们的Hausdorff维数相等.     

N维欧氏空间中一类Sierpinski尘的Hausdorff测度

用相当简洁的初等办法，求出了维n欧氏空间中一类Sierpinski尘的Hausdorff测度的精确值．     

The pointwise dimensions of Moran measures

In this paper,we get the formulas of upper(lower) pointwise dimensions of some Moran measures on Moran sets in Rd under the strong separation condition.We also obtain formulas for the dimension of the Moran measures.Our results extend the known results of some self-similar measures and Moran measures studied by Cawley and Mauldin.     

On the structures and dimensions of Moran sets

The Moran sets and the Moran class are defined by geometric fashion that distinguishes the classical self_similar sets from the following points:(i) The placements of the basic sets at each step of the constructions can be arbitrary.(ii) The contraction ratios may be different at each step.(iii) The lower limit of the contraction ratios permits zero.The properties of the Moran sets and Moran class are studied, and the Hausdorff, packing and upper Box_counting dimensions of the Moran sets are determined by net measure techniques. It is shown that some important properties of the self_similar sets no longer hold for Moran sets.     

Pointwise dimensions of general Moran measures with open set condition

Recently Lou and Wu obtained the formulas of pointwise dimensions of some Moran measures on Moran sets in Rd under the strong separation condition.In this paper,we prove that the result is still true under the open set condition.Due to the lack of the strong separation condition,our approach is essentially different from that used by Lou and Wu.We also obtain the formulas of the Hausdorff and packing dimensions of the Moran measures and discuss some interesting examples.     

The local dimensions of some Moran measures with open set condition

Dai and Liu obtained the formula of local dimensions of some Moran measures on Moran sets in R^d under the strong separation condition. In this paper, we prove that the result is still true under the open set condition. Due to the lack of the strong separation condition, our approach is essentially different to that used by Dai and Liu. We also obtain the formulas of the Hausdorff and packing dimensions of the Moran measures and discuss some interesting examples.     

Quantization dimension function and Gibbs measure associated with Moran set

In this paper we consider the Gibbs measure on the one-sided shift dynamical system and determine the quantization dimension function for the image measure supported on a Moran set. A relationship between the quantization dimension function and the temperature function of the thermodynamic formalism arising in multifractal analysis is also established.     

Classification of Moran fractals

In the paper, we try to classify Moran fractals by using the quasi-Lipschitz equivalence, and prove that two regular homogeneous Moran sets are quasi-Lipschitz equivalent if and only if they have the same Hausdorff dimension.     

一类Moran集的拟对称packing极小性

本文研究Moran集的拟对称packing极小性.利用质量分布原理,证明了实直线上一类特殊的Moran集为拟对称packing极小集,在一定条件下推广了以前文献的结果.