Author/Authors :
Ma، نويسنده , , Yong and Dong، نويسنده , , Xin-Han and Deng، نويسنده , , Qi-Rong، نويسنده ,
Abstract :
In the paper, we mainly discuss the connectedness of two kinds of self-affine sets. One is generated by matrix A = ( p 0 − a q ) and digit set D = { ( i s , j t ) T : i = 0 , 1 , … , | q | − 1 , j = 0 , 1 , … , | p | − 1 } , where s , t ≠ 0 and p , q ∈ Z with 3 ≤ | p | + 1 < | q | < 2 | p | − 1 . The other is generated by matrix A = ( p 0 − a q ) and digit set D = { ( i s , ( d i + j ) t ) T : i = 0 , 1 , … , | p | − 1 , j = 0 , 1 , … , | q | − 1 } , where s , t ≠ 0 , and p , q , d ∈ Z with | p | , | q | ≥ 2 . The sufficient or necessary conditions for their connectedness are revealed.
