Scrambled sets for subshift of finite type
WU Hong-ying · Journal of Guangzhou University · 2010
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,σA) determined by a matrix A that each element of l row and each element of l column is 1 where l ∈{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 e 0 such that every maximal (F 1,F 2)-e-scrambled set of the subshift has cardinality c,where F 1 and F 2 are two compatible to (∑A ×∑A,σA × σA) and kBF 1,kBF 2.