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.     

一类随机Moran集的分形维数

本文研究了随机压缩向量满足一定条件下的随机Moran集的分形维数.利用计算上盒维数的上界和分形维数之间的性质,得到Moran集各种分形维数. 并在一般情形下,给出随机Moran集的上盒维数的上界.     

齐次集及其拟Lipschitz等价

本文定义并研究一类齐次分形,该类分形包含所有的(拟)Ahlfors-David正则集和许多非正则的Moran集,这里如果一个分形的Hausdorff维数与packing维数不相等,则称它是非正则的.对于这类齐次分形,本文得出它们的分形维数,并且给出在适当分离条件下两个齐次分形拟Lipschitz等价的充要条件.随后,本文将这些结果应用到非正则的Moran集上.     

有限义性质下一类广义MORAN集的重分形分解

本文在一类广义Moran集上定义了一种弱分离条件－有限交性质,并证明了重分形分解在广泛的一类分形上仍然成立。本文部分的推广了Cawley和Manlain的结果。     

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。     

关于一维Moran集Hausdorff维数的一个新证明和 一个新结果

利用分形儿何中的技巧给出了关于一维Moran集Hausdorff维数的一个新证明和一个新结果,这可看做是对原有结果的一个有益补充.     

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.     

Sums of moran sets

We find conditions on the dissection of Moran set so that the group it generates under addition has positive Lebesgue measure.     

Hausdorff dimension of Moran sets with increasing spacing

For a family of homogeneous Moran sets, where at each level, subintervals are arranged with in-creasing spaces between neighboring subintervals from left to right, we obtained a formula of the Hausdorff dimensions.     

The multifractal spectrum of some moran measures

The multifractal formalism is shown to hold for a class of Moran measures supported on the Moran fractals associated with the sequences of which the frequency of the letter exists.     

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.     

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.     

Some fractals associated with Cantor expansions

In this paper, we consider a class of fractals generated by the Cantor series expansions. By constructing some homogeneous Moran subsets, we prove that these sets have full dimension.     

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.     

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.     

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.     

Certain Fixed Point Theorems and Application to the Fractal Space

In this paper, we present some important generalizations of the Banach contraction principle, in which the Lipschitz constant k is replaced by some real-valued control function. For the applications to...