数学研究
數學研究
수학연구
JOURNAL OF MATHEMATICAL STUDY
2003年
2期
117-123,132
,共8页
符号空间%有限型子转移%混沌集%Hausdorff测度%Parry测度
符號空間%有限型子轉移%混沌集%Hausdorff測度%Parry測度
부호공간%유한형자전이%혼돈집%Hausdorff측도%Parry측도
symbolic space%subshift of finite type%chaotic set%hausdorff measure%parry measure
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-维的Hausdorff测度.
設A是一箇每列至少有二箇元素為1的不可約0,1方陣,(∑A,σA)為由A所決定的符號空間有限型子轉移. 在∑A上定義一箇與其拓撲相容的度量d使得(∑A,d)的Hausdorff維數為1. 若C是H1-可測的σA的Li-Yorke混沌集,則H1(C)=0;若A是本原的,則存在一箇σA的有限型混沌集S使得H1(S)=1,其中H1為1-維的Hausdorff測度.
설A시일개매렬지소유이개원소위1적불가약0,1방진,(∑A,σA)위유A소결정적부호공간유한형자전이. 재∑A상정의일개여기탁복상용적도량d사득(∑A,d)적Hausdorff유수위1. 약C시H1-가측적σA적Li-Yorke혼돈집,칙H1(C)=0;약A시본원적,칙존재일개σA적유한형혼돈집S사득H1(S)=1,기중H1위1-유적Hausdorff측도.
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.
