CAJ | 학술논문

一般地,对具有重叠结构的自相似集的研究很困难.Rao和Wen研究了具有重叠结构的康托集,Zou等研究了一类具有重叠结构的Sierpinski地毯.他们所研究的集合压缩比分别为r=1/3与1/4.本文将他们的结果推广到一类具有重叠结构的康托集上,其压缩比为r∈Q ∩(0,1/3]之间的有理数.
일반지,대구유중첩결구적자상사집적연구흔곤난.Rao화Wen연구료구유중첩결구적강탁집,Zou등연구료일류구유중첩결구적Sierpinski지담.타문소연구적집합압축비분별위r=1/3여1/4.본문장타문적결과추엄도일류구유중첩결구적강탁집상,기압축비위r∈Q ∩(0,1/3]지간적유리수.
The study of self-similar sets with overlaps is difficult in general. Rao and Wen discussed the Cantor sets with overlaps, Zou et al. studied a class of Sierpinski carpets with overlaps. They studied these sets with contractive ratios r = 1/3 or 1/4,respectively. In this paper, we extend their results to a class of Cantor sets with overlaps when r ∈ Q ∩ (0, 1/3].