符号空间有限型子转移混沌集的Hausdorff测度与Parry测度

设A是一个每列至少有二个元素为1的不可约0，1方阵，(∑4，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G是H^-可测的σA的Li—Yorke混沌集，则H^1(C)＝0；若A是本原的，则存在一个σA的有限型混沌集S使得H^1(S)＝1，其中H^1为1-维的Hausdorff测度．

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

Let A=(aij) be an irreducible N×N matrix with aij∈{0, 1} for all i, j. Let (∑A, σA) 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 H1-measurable Li-Yorke chaotic set for σA, then H1(C)=0 where H1 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 σA such that H1(S)=1.