Silvestri, StefanoPérez, Rodrigo A.2024-10-232024-10-232023Silvestri S, Pérez RA. Accessibility of the Boundary of the Thurston Set. Experimental Mathematics. 2023;32(2):405-422. doi:10.1080/10586458.2021.1974984https://hdl.handle.net/1805/44172Consider two objects associated to the Iterated Function System (IFS) {1+𝜆⁢𝑧,−1+𝜆⁢𝑧}: the locus ℳ of parameters 𝜆∈𝔻∖{0} for which the corresponding attractor is connected; and the locus ℳ0 of parameters for which the related attractor contains 0. The set ℳ can also be characterized as the locus of parameters for which the attractor of the IFS {1+𝜆⁢𝑧,𝜆⁢𝑧,−1+𝜆⁢𝑧} contains 𝜆−1. Exploiting the asymptotic similarity of ℳ and ℳ0 with the respective associated attractors, we give sufficient conditions on 𝜆∈∂ℳ or ∂ℳ0 to guarantee it is path accessible from the complement 𝔻∖ℳ.en-USPublisher PolicyIterated Function SystemFractal GeometrySelf-Affine FractalsZero-Sets of Power SeriesArticle