E-viri
Recenzirano
-
Deng, Qi-Rong; Li, Ming-Tian; Yao, Yong-Hua
Journal of mathematical analysis and applications, 02/2023, Letnik: 518, Številka: 2Journal Article
Let K be the attractor of a self-conformal IFS, μ be the corresponding invariant measure for some probability weights and Λ(K) be the union of all trivial connected components of K. Assume that the IFS satisfies the bounded distortion property and the strong open set condition with an open set V whose closure V‾ is a union of finitely many connected components. It is proven that the four statements dimH(K∖Λ(K))<dimH(K), Hs(V∩Λ(K))>0(wheres=dimH(K)), V∩Λ(K)≠∅ and μ(Λ(K))=1 are equivalent. Some weaker conclusions are also given for attractors generated by bi-Lipschitz IFSs.
