Topological Entropy of a Class of Subshifts of Finite Type

In this paper, we construct a special class of subshifts of finite type. By studying the spectral radius of the transfer matrix associated with the subshift of finite type, we obtain an estimation of its topological entropy. Interestingly, we find that the topological entropy of this class of subshifts of finite type converges monotonically to log(n + 1) (a constant only depends on the structure of the transfer matrices) as the increasing of the order of the transfer matrices.     

Simulation of Effective Subshifts by Two-dimensional Subshifts of Finite Type

In this article we study how a subshift can simulate another one, where the notion of simulation is given by operations on subshifts inspired by the dynamical systems theory (factor, projective subaction …). There exists a correspondence between the notion of simulation and the set of forbidden patterns. The main result of this paper states that any effective subshift of dimension d—that is a subshift whose set of forbidden patterns can be generated by a Turing machine—can be obtained by applying dynamical operations on a subshift of finite type of dimension d+1—a subshift that can be defined by a finite set of forbidden patterns. This result improves Hochman’s (Invent. Math. 176(1):131–167, 2009).     

满Parry测度的有限型子集的Hausdorff维数与测度

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.     

有限型子集的Hausdorff测度

给出了有限型子集的Hausdorff测度的一个估计,改进了已有的结果。     

Rates of Recurrence for Zq and Rq Extensions of Subshifts of Finite Type

In this note we give new asymptotic formulae for certain countingfunctions associated to the periodic behaviour of Z^q and R^qextensions of subshifts of finite type. In the case of the Z^qextensions, these strengthen previous estimates of Marcus andTuncel [9]. For both types of extension, our results complementthe central limit type results of Lalley [6]. Our proof requiresthe application of ideas from thermodynamic formalism. Whilstdeveloping this approach, in Section 2, we take the opportunityto present a counter-example to a related conjecture of Coelho-Filho[2].     

Hausdorff Dimension in Convex Bornological Spaces

For non-metrizable spaces the classical Hausdorff dimension is meaningless. We extend the notion of Hausdorff dimension to arbitrary locally convex linear topological spaces and thus to a large class of non-metrizable spaces. This involves a limiting procedure using the canonical bornological structure. In the case of normed spaces the new notion of Hausdorff dimension is equivalent to the classical notion.     

Fractal dimension for fractal structures: A Hausdorff approach revisited

In this paper, we use fractal structures to study a new approach to the Hausdorff dimension from both continuous and discrete points of view. We show that it is possible to generalize the Hausdorff dimension in the context of Euclidean spaces equipped with their natural fractal structure. To do this, we provide three definitions of fractal dimension for a fractal structure and study their relationships and mathematical properties.     

Hausdorff型测度的性质

本文研究维纹(Dimension Print)所对应的Hausdorff型测度ξα(·),α=(α₁,α₂,…α_n)∈Rⁿ⁺ ,得到它与Hausdorff测度的一些关系,利用这些关系我们给出Rⁿ中一个集合E的Hausdorff型测度ξ^α(E)是正有限值的若干判定条件.     

控制调幅波耗散方程的整体吸引子的有限维

§ 1　IntroductionIn this paperwe shall study successively the equationsgiven in [1 ,2 ] .Underthe sameconditions(i.e.the initial boundary value and other conditions) as in[1 ,2 ] ,the upperbound of the dimension of their global attractor will be obtained respectively.Theexistence of the global attractors have been proved in[1 ,2 ] .This paper is organized as follows:In§ 2 ,we derive the Frechet differential of the solution operator s(t) for theperturbed system.In§ 3 ,we show the finite di…     

Weierstrass型函数图象的分形维数

考虑函数f(x)=sum from i=1 to ∞(?)~(-1)φ((?) θ_n)和w(x)=sum from n=1 to ∞(?)φ_(?)((?)x θ_(?)),式中0<α<(?)是任意实数,在一定条件下,估计了函数f图象的Hausdorff维数的下界,并求得了w函数图象的Box维数和Packing维数。     

Strong mixing subshift of finite type and Hausdorff measure of its chaotic set

We present a sufficient and necessary condition for the subshift of finite type to be a measure-preserving transformation or to be a strong mixing measure-preserving transformation with respect to the Hausdorff measure. It is proved that a strong mixing subshift of finite type has a chaotic set with full Hausdorff measure.     

Distributional Dimension of Fraetal Sets in Local Fields

The distributional dimension of fractal sets in R^n has been systematically studied by Triebel by virtue of the theory of function spaces. In this paper, we first discuss some important properties about the B-type spaces and the F-type spaces on local fields, then we give the definition of the distributional dimension dimD in local fields and study the relations between distributional dimension and Hausdorff dimension. Moreover, the analysis expression of the Hausdorff dimension is given. Lastly, we define the Fourier dimension in local fields, and obtain the relations among all the three dimensions. Keywords local field, B-type space, F-type space, distributional dimension, Hausdorff dimension Fourier dimension     

Hausdorff dimension and doubling measures on metric spaces

Volberg and Konyagin have proved that a compact metric space carries a nontrivial doubling measure if and only if it has finite uniform metric dimension. Their construction of doubling measures requires infinitely many adjustments. We give a simpler and more direct construction, and also prove that for any , the doubling measure may be chosen to have full measure on a set of Hausdorff dimension at most .

     

一类分形函数的Weyl-Marchaud分数阶导数的Hausdorff维数

首先介绍广义Weierstrass型函数的Weyl-Marchaud分数阶导数,得到了带随机相位的广义Weierstrass型函数的Weyl-Marchaud分数阶导数图像的Hausdorff维数,证明了该分形函数图像的Hausdorff维数与Weyl-Marchaud分数阶导数的阶之间的线性关系.     

Bush型函数的分形维数及其奇异性

本文给出了一类无处可微的连续函数──Ｂｕｓｈ型函数的Ｂｏｘ维数的精确值及其Ｈａｕｓｄｏｒｆｆ维数的下界估计值，同时讨论了Ｂｕｓｈ型函数的奇异性特征．     

有限个GO-空间乘积的遗传集体Hausdorff性(英文)

本文证明了最小线性序紧化中点的共尾数不超过ω₁的有限个GO-空间的乘积是遗传集体Hausdorff空间。     

Factorization theorems for cohomological dimension

The well-known factorization theorems for covering dimension dim and compact Hausdorff spaces are here established for the cohomological dimension dim using a new characterization of dim In particular, it is proved that every mapping f: X → Y from a compact Hausdorff space X with to a compact metric space Y admits a factorization f = hg, where g: X → Z, h: Z → Y and Z is a metric compactum with . These results are applied to the well-known open problem whether . It is shown that the problem has a positive answer for compact Hausdorff spaces X if and only if it has a positive answer for metric compacta X.     

加权Besicovitch集的Hausdorff维数

本文引入并研究符号空间上的加权Besicoritch集.通过构造一个伯努利测度,得到此集的Hausdorff维数,结果符合一个变分原理.     

非自治Schrdinger-KdV型藕合方程组的一致吸引子及其维数估计

本文研究了非自治Schrodinger-KdV型藕合方程组的非线性动力学行为．运用具有两个参数的算子簇来描述非自治无穷维动力系统的方法，证明了该系统的一致吸引子的存在性．进一步，对其Hausdorff维数进行了估计．