Hausdorff centred measure of non-symmetry cantor sets
Tóm tắt
Let 0<λ1,λ2<1 and 1λ1-λ2≥ max {λ1,λ2}. Let (λ1,λ2) be the attractor of the iterated function system {φ1,φ2} on the line, where φ1(itx)=λ1
x and φ2(x)=1−λ1+λ1
x,x∈R. K(λ1,λ2) is called a non-symmetry Cantor set. In this paper, it is proved that the exact Hausdorff centred measure of K(λ1,λ2) equals 2
s
(1−λ)
s
, where λ=max{λ1,λ2} and s is the Hausdorff dimension of K(λ1,λ2).
Từ khóa
Tài liệu tham khảo
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