LetΨ={ψn}n≥1 be an iterated function system(IFS)on[0,1]with attractor J.Associated with each x∈J,there is a sequence{ωn(x)}n≥1 consisting of integers,called the digit sequence of x,such that■((1))We revisit the...LetΨ={ψn}n≥1 be an iterated function system(IFS)on[0,1]with attractor J.Associated with each x∈J,there is a sequence{ωn(x)}n≥1 consisting of integers,called the digit sequence of x,such that■((1))We revisit the Borel-Bernstein theorem in a d-decaying Gauss-like IFS,and completely characterize the metrical properties of the set■whereΦ:ℕ→ℝis a positive function.展开更多
基金supported by the Scientific Research Project of Colleges and Universities in Anhui Province(2024AH050016)supported by the NSFC(12171172).The third author was supported by the NSFC(12201476)the Fundamental Research Funds for the Central Universities.
文摘LetΨ={ψn}n≥1 be an iterated function system(IFS)on[0,1]with attractor J.Associated with each x∈J,there is a sequence{ωn(x)}n≥1 consisting of integers,called the digit sequence of x,such that■((1))We revisit the Borel-Bernstein theorem in a d-decaying Gauss-like IFS,and completely characterize the metrical properties of the set■whereΦ:ℕ→ℝis a positive function.
