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On quasi-weakly almost periodic points

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Science China Mathematics 2013年第3期56卷 597-606页

作者： HE WeiHong YIN JianDong zhou zuoling School of Mathematics and Computational Science Sun Yat-sen University Department of Mathematics Nanchang University Lingnan College Sun Yat-sen University University

The core problem of dynamical systems is to study the asymptotic behaviors of orbits and their topological structures. It is well known that the orbits with certain recurrence and generating ergodic (or invariant) measures are important, such orbits form a full measure set for all invariant measures of the system, its closure is called the measure center of the system. To investigate this set, zhou introduced the notions of weakly almost periodic point and quasi-weakly almost periodic point in 1990s, and presented some open problems on complexity of discrete dynamical systems in 2004. One of the open problems is as follows: for a quasi-weakly almost periodic point but not weakly almost periodic, is there an invariant measure generated by its orbit such that the support of this measure is equal to its minimal center of attraction (a closed invariant set which attracts its orbit statistically for every point and has no proper subset with this property)? Up to now, the problem remains open. In this paper, we construct two points in the one-sided shift system of two symbols, each of them generates a sub-shift system. One gives a positive answer to the question above, the other answers in the negative. Thus we solve the open problem completely. More important, the two examples show that a proper quasi-weakly almost periodic orbit behaves very differently with weakly almost periodic orbit.

关键词： weakly almost periodic point quasi-weakly almost periodic point minimal center of attraction

A THEORETICAL FRAMEWORK FOR THE CALCULATION OF HAUSDORFF MEASURE-SELF—SIMILAR SET SATISFYING OSC

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Analysis in Theory and Applications 2011年第4期27卷 387-398页

作者： zuoling zhou Li Feng Sun Yat-Sen University China Albany State University USA

A theoretical framework for the calculation of Hausdorff measure of self-similar sets satisfying OSC has been established.

关键词： Haudorff measure open set condition

SOME PROBLEMS ON FRACTAL GEOMETRY AND TOPOLOGICAL DYNAMICAL SYSTEMS

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Analysis in Theory and Applications 2009年第1期25卷 5-15页

作者： zuoling zhou Feng Li Lingnan Collge Sun Yat-sen University Guangzhou 510275 P. R. China Department of Mathematics and Computer Science Albany State University Albany GA 31705 USA

This paper is a continuation of [14], some new problems on fractal geometry and topological dynamical systems have been posed.

关键词： fractal geometry topological dynamical system

THE EXACT MEASURES OF A CLASS OF SELF-SIMILAR SETS ON THE PLANE

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Analysis in Theory and Applications 2008年第2期24卷 160-182页

作者： Zhiwei Zhu zuoling zhou Department of MathematicsZhaoqing UniversityZhaoqing 526061 P. R. China Lingnan CollegeZhongshan UnivesityGuangzhou 510275 P. R. China

Let S belong to R^2 be the attractor of the iterated function system {f1, f2, f3 } iterating on the unit equilateral triangle So. where fi（x） =λix ＋ bi, i = 1,2, 3, x =（x1, x2）, b1=（0, 0）, b3=（1-λ3 /2,√3/2 （1-λ3）） This paper determines the exact Hausdorff measure, centred covering measure and packing measure of S under some conditions relating to the contraction parameter.

关键词： self-similar set Hausdorff measure centred covering measure packing measure

ON THE EXACT HAUSDORFF MEASURE OF A CLASS OF SELF-SIMILAR SETS SATISFYING OPEN SET CONDITION

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Analysis in Theory and Applications 2008年第1期24卷 93-100页

作者： Shaoyuan Xu Weiyi Su zuoling zhou Huaibei Coal Industry Teachers College China Nanjing University China Zhongshan University China

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-simila... 详细信息

关键词： self-similar set Hausdorff measure and Hausdorff dimension open set condition

A NEW LOWER BOUND OF THE HAUSDORFF MEASURE OF THE SIERPINSKI GASKET

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Analysis in Theory and Applications 2006年第1期22卷 8-19页

作者： Zhiwei Zhu zuoling zhou Baoguo Jia Zhaoqing University China Zhongshan University Ghina

For the Sierpinski gasket, by using a sort of cover consisting of special regular hexagons, we define a new measure that is equivalent to the Hausdorff measure and obtain a lower bound of this measure. Moreover, the following lower bound of the Hausdroff measure of the Sierpinski gasket has been achieved H^s（S）≥0.670432,where S denotes the Sierpinski gasket, s = dimn（S） = log23, and H^s（S） denotes the s-dimensional Hausdorff measure of S. The above result improves that developed in .

关键词： Hausdorff measure regular hexagonal cover Sierpinski gasket

Some Results on the Upper Convex Densities of the Self-Similar Sets at the Contracting-Similarity Fixed Points

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Analysis in Theory and Applications 2015年第1期31卷 92-100页

作者： Shaoyuan Xu Wangbin Xu zuoling zhou School of Maths and Statistics Hanshan Normal University School of Maths and Statistics Hubei Normal University School of Lingnan Zhongshan University

In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets at the contracting-similarity fixed points is given. Next, under the strong separation open set condition, the existence of the best shape for the upper convex densities of self-similar sets at the contracting-similarity fixed points is proven. As consequences, an open problem and a conjecture, which were posed by zhou and Xu, are answered.

关键词： Self-similar set upper convex density Hausdorff measure and Hausdorff dimension,contracting-similarity fixed point.

A Local Property of Hausdorff Centered Measure of Self-Similar Sets

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Analysis in Theory and Applications 2014年第2期30卷 164-172页

作者： Zhiwei Zhu zuoling zhou College of Mathematics and Statistics Zhaoqing University Lingnan College Sun Yat-Sen University

We analyze the local behavior of the Hausdorff centered measure for self- similar sets. If E is a self-similar set satisfying the open set condition, thenC^s（E∩B（x,r））≤（2r）^sfor all x ∈ E and r〉 0, where Cs denotes the s-dimensional Hausdorff centered measure. The above inequality is used to obtain the upper bound of the Hausdorff centered measure. As the applications of above inequality, We obtained the upper bound of the Hausdorff centered measure for some self-similar sets with Hausdorff dimension equal to 1, and prove that the upper bound reach the exact Hausdorff centered measure.

关键词： Hausdorff centered measure Hausdorff measure self-similar sets.

PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES

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Acta Mathematica Scientia 2024年第4期44卷 1327-1336页

作者： zuoling LIU Hasi WULAN Department of Mathematics Shantou UniversityShantou 515063China

For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.

关键词： compactness boundedness Bloch type space product type operator weighted Bergman space