有限型子转移的攀援集

Scrambled sets for subshift of finite type

研究了有限型子转移攀援集的"大小".证明了对于第l行和第l列全为1的N阶0,1方阵所决定的有限型子转移而言,其中l∈{0,1,…,N-1},若它有正拓扑熵,则它的每一个极大Li-Yorke攀援集的基数为c;对于每行至少有两个元素为1且1在对角线上至少出现两次的N阶0,1方阵所决定的有限型子转移而言,若它是拓扑传递的,则存在ε>0,使得它的每一个极大(F1,F2)-ε-攀援集的基数为c,其中F1与F2是与它的乘积系统兼容的Furstenberg族且kBF1,kBF2.

This paper deals with the topological size of scrambled sets with respect to subshifts of finite type determined by an N × N matrix A = （aij） with aij ∈ { 0,1 } In terms of subshifts of finite type （ A,O＇A ） determined by a matrix A that each element of 1 row and each element of l column is 1 where l E { 0,1 ,……N - 1} , we show that every maximal scrambled set of the subshift has cardinality c if it has positive topological entropy. Moreover, in terms of subshifts of finite type （∑A, σA ） determined by a matrix A that every row has at least two elements of 1 and 1 appears twice on the diagonal line, we point out if it is topologically transitive, then there exists a ε 〉 0 such that every maximal （F1,F2） -ε-scrambled set of the suhshift has cardinality c, where F1 and F2 are two compatible to （ ∑A × ∑A, σA × σA） and k R（belong to） F1,k R（belong to）F2.