共查询到20条相似文献,搜索用时 15 毫秒
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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
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In this article,the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions.Several examples are given at the end. 相似文献
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本文确定了保形图递归集的 Hausdorff维数,证明了相应的 Hausdorff度是正σ-有限的,并且我们给出了 Hausdorff测度为正有限的充分必要条件. 相似文献
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All the full Parry measure subsets of a given subshift of finite type determined by an irreducible 0-1 matrix have the same Hausdorrf dimension and Hausdorff measure which coincide with those of the set of finite type. 相似文献
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Yueyun Hu 《Journal of Theoretical Probability》1999,12(2):313-346
Burdzy and Khoshnevisan(9) have shown that the Hausdorff dimension of the level sets of an iterated Brownian motion (IBM) is equal to 3/4. In this paper, the exact Hausdorff measure function and the packing measure of the levels set of IBM are given. Our approach relies on some accurate analysis on the local asymptotic of local times. 相似文献
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研究了N指标d维广义Wiener过程像集的一致维数和测度,得到了其像集的致Hausdorff维数和一致Packing维数。 相似文献
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In this paper,we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition(OSC).As applications,we discuss a self-similar Cantor set satisfying OSC and give a simple method for computing its exact Hausdorff measure. 相似文献
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设S_λ为压缩比为λ(λ≤1/3)的一类Sierpinski垫,s=-log_λ3为S_λ的Hausdorff维数,N为产生S_λ的所有基本三角形的集合.本文使用网测度方法,获得了S_λ的s-维Hausdorff测度的精确值H~s(S_λ)=1,同时证明了H~s(S_λ)可由S_λ关于网N的s-维Hausdorff测度H_N~s(S_λ)确定,获得了S_λ的非平凡的最佳覆盖. 相似文献
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A very important property of a deterministic self-similar set is that its Hausdorff dimension and upper box-counting dimension coincide. This paper considers the random case. We show that for a random self-similar set, its Hausdorff dimension and upper box-counting dimension are equal
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《Indagationes Mathematicae》2019,30(5):862-873
An approach is given for estimating the Hausdorff dimension of the univoque set of a self-similar set. This sometimes allows us to get the exact Hausdorff dimensions of the univoque sets. 相似文献
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Balázs Bárány 《Journal of Mathematical Analysis and Applications》2011,383(1):244-258
The dimension theory of self-similar sets is quite well understood in the cases when some separation conditions (open set condition or weak separation condition) or the so-called transversality condition hold. Otherwise the study of the Hausdorff dimension is far from well understood. We investigate the properties of the Hausdorff dimension of self-similar sets such that some functions in the corresponding iterated function system share the same fixed point. Then it is not possible to apply directly known techniques. In this paper we are going to calculate the Hausdorff dimension for almost all contracting parameters and calculate the proper dimensional Hausdorff measure of the attractor. 相似文献
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Siegfried GRAF在文献[1]中给出了自相似集上的Hausdorff测度(简称H-测度)的特征.John McLaughlin在文献[2]中引入了拟相似集的概念,K.J.Falconer又在文献[3]中讨论了拟相似集上H-测度和维数的性质.本文研究拟相似集上的H-测度的特征,并得出在一定条件下支撑于其上满足一定条件的测度与H-测度的等价性条件. 相似文献
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作者进一步研究了在文章[1]中构造的广义统计自相似集的分形性质,得到了这类集合的Hausdorff维数和确切Hausdorff测度函数。文中的结果是[4]中结果的延拓。 相似文献
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1 IntroductionTherehasbeenconsiderableinterestinfractals,bothintheiroccurrenceinthesciences,andintheirmathematicaltheory .Awideclassoffractalsetsaregeneratedbyiteratedfunc tionsystem .Aself similarsetinRdisacompactsetKfulfillingtheinvarianceK =∪Ni=1 SiK ,whereS1,S2 ,… ,SNarecontractivesimilarities.IfS1,S2 ,… ,SNarecontractiveconfor malmappings,weobtainself conformalset.Itiswell known(seeHutchinson [1 2 ] )that,givenafamilyofsuchmappings,thereisauniquecompactsetwiththisproperty .Ifth… 相似文献
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Wolfgang Kreitmeier 《分析论及其应用》2010,26(1):84-100
Let d ≥ 1 be an integer and E a self-similar fractal set, which is the attractor of a uniform contracting iterated function system (UIFS) on R
d
. Denote by D the Hausdorff dimension, by H
D
(E) the Hausdorff measure and by diam(E) the diameter of E. If the UIFS is parametrised by its contracting factor c, while the set ω of fixed points of the UIFS does not depend on c, we will show the existence of a positive constant depending only on ω, such that the Hausdorff dimension is smaller than one and H
D
(E) = diam(E)
D
if c is smaller than this constant. We apply our result to modified versions of various classical fractals. Moreover, we present
a parametrised UIFS, where ω depends on c and show the inequatily H
D
(E) < diam(E)
D
, if c is small enough. 相似文献
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关于三分Cantor集的构造的一个基本性质及其应用 总被引:13,自引:0,他引:13
本文提出了三分 Cantor集的构造的一个基本性质 .作为应用 ,给出了计算三分 Cantor集的简明的初等的计算方法 ,另外还得到了一列有趣的对数不等式 相似文献