符号空间有限型子转移混沌集的Hausdorff测度与Parry测度(英文)

Hausdorff Measure and Parry Measure of Chaotic Sets of Subshift of Finite Type in Symbolic Space

设A是一个每列至少有二个元素为 1的不可约 0 ,1方阵 ,(∑A,σA)为由A所决定的符号空间有限型子转移 .在∑A 上定义一个与其拓扑相容的度量d使得 (∑A,d)的Hausdorff维数为 1.若C是H1 可测的σA 的Li Yorke混沌集 ,则H1(C) =0 ;若A是本原的 ,则存在一个σA 的有限型混沌集S使得H1(S)=1,其中H1为 1

Let A=(a ij) be an irreducible N×N matrix with a ij∈{0, 1} for all i, j. Let (∑ A, σ A) be a subshift of finite type determined by the matrix A. We define a metric d on ∑ A, then we have results as follow: Suppose every column of A has at least two 1. If C is a H 1-measurable Li-Yorke chaotic set for σ A, then H 1(C)=0 where H 1 denotes 1-dimension Hausdorff measure on (∑ A, d); If A is an irreducible and aperiodic matrix, then there is a finite chaotic set S for σ A such that H 1(S)=1.