共查询到19条相似文献,搜索用时 93 毫秒
1.
满足强分离条件的自相似集的填充测度 总被引:1,自引:0,他引:1
对满足强分离条件的自相似集,本文给出一种估计填充测度下界的方法,称为部分估计原理.利用这种估计方法得出的某些自相似集的填充测度的下界,往往和准确的填充测度值相等. 相似文献
2.
由表示系统生成的分形的维数 总被引:3,自引:2,他引:1
在这篇文章里,由Rn中点的表示系统所生成的自仿射集中,给出了自仿射集满足Moran开集条件的一个新的判别方法和不满足开集条件的自相似集的Hausdorff维数的上界和下界,并根据两个实例估计出其上下界是相等的. 相似文献
3.
关于自相似集的Hausdorff测度的一个判据及其应用 总被引:6,自引:1,他引:5
讨论了满足开集条件的自相似集。对于此类分形,用自然覆盖类估计它的Hausdorff测度只能得到一个上限,因而如何判断某一个上限就是它的Hausdorff测度的准确值是一个重要的问题。本文给出了一个判据。作为应用,统一处理了一类自相似集,得到了平面上的一个Cantor集-Cantor尘的Hausdorff测度的准确值,并重新计算了直线上的Cantor集以及一个Sierpinski地毯的Hausdorff测度。 相似文献
4.
5.
本文讨论利用上、下球密度计算自相似集的Hausdorff中心测度与填充测度的问题.设E是满足强分离条件的自相似集,s为其Hausdorff维数,μ为定义于E上的自相似测度,则有如下结论:(1)如果存在x0∈E,使得x0关于μ的上球密度■(μ,x0)=■,则对μ-几乎所有x∈E,有■(μ,x)≥■;(2)如果存在y0∈E,使得y0关于μ的下球密度■(μ,y0)=■,则对μ-几乎所有y∈E,有■(μ,g)≤■.运用这一结论,对自相似集的测度计算问题进行了讨论. 相似文献
6.
该文讨论满足开集条件的自相似集上的马尔科夫测度,给出了马尔科夫测度具有加倍性质的一个充分必要条件.作为应用,刻画了几个具体的自相似集上具有加倍性质的马尔科夫测度. 相似文献
7.
8.
讨论满足开集条件的自相似集 .对于这样一个分形 ,用定义估计它的Haus dorff测度只能得到上限 ,因而如何判断某一个上限是否就是它的准确值是一个重要问题.给出了一个否定判据 .作为应用 ,否定了Marion关于Koch曲线的Hausdorff测度的猜测. 相似文献
9.
本文研究了一类关于自相似测度绝对连续的概率测度的点密度测度的问题.利用迭代函数系,量子系数和H(o|¨)lder不等式,在自相似集满足强分离条件下,获得了此点密度测度,推广了自相似测度为Lebesgue测度的结果. 相似文献
10.
11.
We obtain the equivalence conditions for an on-diagonal upper bound of heat kernels on self-similar measure energy spaces. In particular, this upper bound of the heat kernel is equivalent to the discreteness of the spectrum of the generator of the Dirichlet form, and to the global Poincaré inequality. The key ingredient of the proof is to obtain the Nash inequality from the global Poincaré inequality. We give two examples of families of spaces where the global Poincaré inequality is easily derived. They are the post-critically finite (p.c.f.) self-similar sets with harmonic structure and the products of self-similar measure energy spaces. 相似文献
12.
In-Soo Baek 《Journal of Mathematical Analysis and Applications》2004,292(1):294-302
A self-similar Cantor set is completely decomposed as a class of the lower (upper) distribution sets. We give a relationship between the distribution sets in the distribution class and the subsets in a spectral class generated by the lower (upper) local dimensions of a self-similar measure. In particular, we show that each subset of a spectral class is exactly a distribution set having full measure of a self-similar measure related to the distribution set using the strong law of large numbers. This gives essential information of its Hausdorff and packing dimensions. In fact, the spectral class by the lower (upper) local dimensions of every self-similar measure, except for a singular one, is characterized by the lower or upper distribution class. Finally, we compare our results with those of other authors. 相似文献
13.
关于自相似集的Hausdorff测度 总被引:12,自引:0,他引:12
得到了 Hausdorff容度与 Hausdorff测度相等的集的充分必要条件.对于满足开集条件的自相似集,验证了它的Hausdorff容度与Hausdorf测度相等并给出了它的Hausdorff测度的一个便于应用的公式.作为例子,给出了均匀康托集的Hausdorff测度的一种新的计算方法,对于Koch曲线的Hausdorff测度的上限也作了讨论. 相似文献
14.
L. Olsen 《Mathematische Nachrichten》2009,282(10):1461-1477
By now the multifractal structure of self-similar measures satisfying the so-called Open Set Condition is well understood. However, if the Open Set Condition is not satisfied, then almost nothing is known. In this paper we prove a nontrivial lower bound for the symbolic multifractal spectrum of an arbitrary self-similar measure. We emphasize that we are considering arbitrary self-similar measures (and sets) which are not assumed to satisfy the Open Set Condition or similar separation conditions. Our results also have applications to self-similar sets which do not satisfy the Open Set Condition (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
The Moran fractal considered in this paper is an extension of the self-similar sets satisfying the open set condition. We consider those subsets of the Moran fractal that are the union of an uncountable number of sets each of which consists of the points with their location codes having prescribed mixed group frequencies. It is proved that the Hausdorff and packing dimensions of each of these subsets coincide and are equal to the supremum of the Hausdorff (or packing) dimensions of the sets in the union. An approach is given to calculate their Hausdorff and packing dimensions. The main advantage of our approach is that we treat these subsets in a unified manner. Another advantage of this approach is that the values of the Hausdorff and packing dimensions do not need to be guessed a priori. 相似文献
16.
We prove that there exist self-similar sets of zero Hausdorff measure, but positive and finite packing measure, in their dimension;
for instance, for almost everyu ∈ [3, 6], the set of all sums ∑
0
8
a
n
4−n
a
n
4−n
with digits witha
n
∈ {0, 1,u} has this property. Perhaps surprisingly, this behavior is typical in various families of self-similar sets, e.g., for projections
of certain planar self-similar sets to lines. We establish the Hausdorff measure result using special properties of self-similar
sets, but the result on packing measure is obtained from a general complement to Marstrand’s projection theorem, that relates
the Hausdorff measure of an arbitrary Borel set to the packing measure of its projections.
Research of Y. Peres was partially supported by NSF grant #DMS-9803597.
Research of K. Simon was supported in part by the OTKA foundation grant F019099.
Research of B. Solomyak was supported in part by NSF grant #DMS 9800786, the Fulbright Foundation, and the Institute of Mathematics
at The Hebrew University of Jerusalem. 相似文献
17.
On the symbolic space endowed with a metric given by a Gibbsmeasure, it is shown that, for any invariant probability measureµ other than the given Gibbs measure, the set of µ-genericalpoints satisfies a zero-infinity law (in particular,its Hausdorff and packing measure are infinite). This extendsa result of R. Kaufman on BesicovitchEggleston sets,and applies to level sets of Birkhoff averages and certain subsetsof self-similar sets. 相似文献
18.
GEOMETRY AND DIMENSION OF SELF—SIMILAR SET 总被引:1,自引:0,他引:1
The authors show that the self-similar set for a finite family of contractive similitudes (similarities, i.e., |fi(x) - fi(y)| = αi|x - y|, x,y ∈ RN, where 0 < αi < 1) is uniformly perfect except the case that it is a singleton. As a corollary, it is proved that this self-similar set has positive Hausdorff dimension provided that it is not a singleton. And a lower bound of the upper box dimension of the uniformly perfect sets is given. Meanwhile the uniformly perfect set with Hausdorff measure zero in its Hausdorff dimension is given. 相似文献