共查询到20条相似文献,搜索用时 468 毫秒
1.
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. 相似文献
2.
Jinjun Li 《Nonlinear Analysis: Real World Applications》2012,13(1):348-358
Dai and Liu obtained the formula of local 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 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. 相似文献
3.
此文考虑了一类Moran分形,在其生成过程中每一阶的压缩比及压缩比的个数可以是不相同的,证明了支撑在此类Moran分形上的Moran测度的L^q-谱的存在性. 相似文献
4.
On the structures and dimensions of Moran sets 总被引:6,自引:0,他引:6
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. 相似文献
5.
The multifractal spectrum of some moran measures 总被引:3,自引:0,他引:3
WU Min School of Mathematical Sciences South China University of Technology Guangzhou China 《中国科学A辑(英文版)》2005,48(8):1097-1112
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. 相似文献
6.
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. 相似文献
7.
8.
Yi Wang 《Journal of Mathematical Analysis and Applications》2009,354(2):445-450
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. 相似文献
9.
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. 相似文献
10.
11.
苏峰 《数学物理学报(A辑)》2001,21(2):211-214
该文考虑广义Moran集的重分形分解问题,讨论了在不附加压缩尺度具有正的下界条件的情形下广义Moran集的重分形分解集的Hausdorff维数问题. 相似文献
12.
13.
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. 相似文献
14.
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. 相似文献
15.
16.
给定Rd 中的Moran集类 ,本文证明了对介于该集类中元素的上盒维数的最大值和最小值之间的任何一个数值s,总存在该集类中的一个元素 ,其上盒维数等于s,对下盒维数、修正的下盒维数也有类似的性质成立 ,从而给文 [1 ]中的猜想 1一个肯定的回答 .此外 ,还讨论了齐次Cantor集和偏次Cantor集盒维数存在性之间的关系 . 相似文献
17.
San Guo Zhu 《数学学报(英文版)》2019,35(9):1520-1540
Let E be a Moran set on ℝ1 associated with a bounded closed interval J and two sequences 相似文献
18.
本文研究了填充维数与上盒维数的关系.利用Cantor-Bendixson定理的方法,得到了由上盒维数给出的填充维数的等价定义.并证明了齐次Moran集对上盒维数和填充维数的连续性. 相似文献
19.
Mrinal Kanti Roychowdhury 《Journal of Mathematical Analysis and Applications》2011,373(1):73-505
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. 相似文献
20.
TheHAUSDORFFDIMENSIONANDMEASUREOFTHEGENERALIZEDMORANFRACTALSANDFOURIERSERIES¥RENFUThO;LIANGJINRONGAbstract:Thispaperstudiesth... 相似文献