A Class Of Linear Cantor Sets With Overlaps

Let E_λ be the attractor of the contractive IFS S₀(x) = x/7,S₁(x) = (x + _λ)/7, S₂(x) = (x + 2)/7, S₃(x) = (x + 4 - λ)/7, S₄(x) = (x + 6 - 2λ)/7 and S₅(x) = (x + 6)/7 with λ ∈ [0,1] ∩ Q. In this paper,the geometric structure and the Hausdorff dimension of E_λ are discussed.