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hausdorff dimension of Julia set of a polynomial with a Siegel disk

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Science China Mathematics 2006年第9期49卷 1284-1296页

作者： SHEN Liang LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China LMAM School of Mathematical Sciences Peking University Beijing China

Let f(z) = e2πiθz(1+z/d)d,θ∈R\Q be a polynomial. Ifθis an irrational number of bounded type, it is easy to see that f(z) has a Siegel disk centered at 0. In this paper, we will show that the hausdorff dimension o... 详细信息

关键词： hausdorff dimension Siegel disk porous set

hausdorff dimension and Measure of a Class of Subsets of the General Sierpinski Carpets

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Acta Mathematica Sinica,English Series 2010年第7期26卷 1369-1382页

作者： Yong Xin GUI Department of Mathematics Xianning College Xianning 437100 P. R. China Department of Mathematics East China Normal University Shanghai 200062 P. R. China

In this paper we study a class of subsets of the general Sierpinski carpets for which two groups of allowed digits occur in the expansions with proportional frequency. We calculate the hausdorff and Box dimensions of these subsets and give necessary and sufficient conditions for the corresponding hausdorff measure to be positive and finite.

关键词： the general Sierpinski carpets hausdorff dimension hausdorff measure

hausdorff dimension of quasi-cirles of polygonal mappings and its applications

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Science China Mathematics 2013年第5期56卷 1033-1040页

作者： HUO ShengJin TANG ShuAn WU ShengJian LMAM and School of Mathematical Sciences Peking University School of Mathematics and Computer Science Guizhou Normal University

We show that the hausdorff dimension of quasi-circles of polygonal mappings is one. Furthermore, we apply this result to the theory of extremal quasiconformal mappings. Let [μ] be a point in the universal Teichmiiller space such that the hausdorff dimension of fμ（δ△） is bigger than one. We show that for every kn ∈ （0, 1） and polygonal differentials δn, n = 1, 2, the sequence {[kn δn/｜δn｜} cannot converge to [μ] under the Teichmiiller metric.

关键词： hausdorff dimension Teichmiiller space quasi-circle polygonal mapping

hausdorff dimension of Moran sets with increasing spacing

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Science China Mathematics 2013年第3期56卷 553-560页

作者： XUE YuMei KAMAE Teturo School of Mathematics and System Sciences LMIB Beihang University Advanced Mathematical Institute Osaka City University

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.

关键词： Moran set hausdorff dimension

hausdorff dimension of self-similar sets with overlaps

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Science China Mathematics 2009年第1期52卷 119-128页

作者： DENG QiRong John HARDING HU TianYou Department of Mathematics Fujian Normal UniversityFuzhou 350007China Department of Mathematical Sciences New Mexico State UniversityLas CrucesNM 88003USA Department of Mathematics University of Wisconsin-Green BayGreen BayWI 54311USA

We provide a simple formula to compute the hausdorff dimension of the attractor of an overlapping iterated function system of contractive similarities satisfying a certain collection of assumptions. This formula is obtained by associating a non-overlapping infinite iterated function system to an iterated function system satisfying our assumptions and using the results of Moran to compute the hausdorff dimension of the attractor of this infinite iterated function system, thus showing that the Hausforff dimension of the attractor of this infinite iterated function system agrees with that of the attractor of the original iterated function system. Our methods are applicable to some iterated function systems that do not satisfy the finite type condition recently introduced by Ngai and Wang.

关键词： hausdorff dimension iterated function system self-similarity 28A78 28A80

hausdorff dimension OF CUTSET OF COMPLEX VALUED RADEMACHER SERIES

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Acta Mathematicae Applicatae Sinica 2000年第2期16卷 140-148页

作者：吴敏 Department of Mathematics Hubei University Wuhan China

Cutsets of series form an important class of fractal sets. In this paper, the author obtains the Hausdoff dimension of outset of complex valued Rademacher serise.

关键词： hausdorff dimension fractal set outset

The hausdorff dimension of Sets Related to the General Sierpinski Carpets

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Acta Mathematica Sinica,English Series 2010年第4期26卷 731-742页

作者： Yong Xin GUI Wen Xia LI Department of Mathematics East China Normal University Shanghai 200241 P. R. China Department of Mathematics Xianning College Xianning 437005 P. R. China

In this paper we study a class of subsets of the general Sierpinski carpets for which the allowed two digits in the expansions occur with proportional frequency. We calculate the hausdorff and box dimensions of these ... 详细信息

关键词： general Sierpinski carpets hausdorff dimension hausdorff measure

hausdorff dimension of a Class ofWeierstrass Functions

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Analysis in Theory and Applications 2020年第4期36卷 482-496页

作者： Huojun Ruan Na Zhang School of Mathematical Sciences Zhejiang UniversityHangzhouZhejiang 310027China

It was proved by Shen that the graph of the classical Weierstrass function∑∞n=0λn cos(2πbnx)has hausdorff dimension 2+logλ/log b,for every integer b≥2 and everyλ∈(1/b,1)[hausdorff dimension of the graph of the classical Weierstrass functions,Math.Z.,289(2018),223-266].In this paper,we prove that the dimension formula holds for every integer b≥3 and everyλ∈2(1/b,1)if we replace the function cos by sin in the definition of Weierstrass function.A class of more general functions are also discussed.

关键词： hausdorff dimension Weierstrass function SRB measure.

Hitting Probabilities and the hausdorff dimension of the Inverse Images of a Class of Anisotropic Random Fields

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Acta Mathematica Sinica,English Series 2015年第12期31卷 1895-1922页

作者： Zhen Long CHEN Quan ZHOU School of Statistics and Mathematics Zhejiang Gongshang University

Let X = {X（t）：t ∈ R^N} be an anisotropic random field with values in R^*** certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively hausdorff measure and Bessel-Riesz *** also obtain the hausdorff dimension of its inverse image,and the hausdorff and packing dimensions of its level *** results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields.

关键词： Anisotropic random field non-linear stochastic heat equations spatially homogeneous Gaussian noise hitting probabilities hausdorff dimension inverse image