数学杂志2024，Vol.44Issue(4)：343-357,15.
Sylvester连分数展式中若干例外集的Hausdorff维数
HAUSDORFF DIMENSIONS OF CERTAIN SETS IN TERMS OF THE SYLVESTER CONTINUED FRACTION EXPANSIONS
摘要
Abstract
For x ∈(0,1],let x=[d1,d2,…]be its Sylvester continued fraction expansions,we calculate the Hausdorff dimension of the set A(ψ)defined in terms of the Sylvester continued fraction expansions as A(ψ)={x∈(0,1]:limn→∞ logdn(x)/ψ(n)=1},where ψ(n)is a positive function defined on N.By constructing the covering and a suitable subset of Cantor,we get the exact Hausdorff dimension of the set as dim H A(ψ)=lim infn→∞ ψ(1)+ψ(2)+…+ψ(n)/ψ(n+1)At the same time,we also calculate the Hausdorff dimension of the set of points with limn→∞logdn(x)/ψ(n)=0 or ∞.关键词
Sylvester连分数/Hausdorff维数/增长速度Key words
Sylvester continued fraction expansions/Hausdorff dimension/growth rate分类
数理科学引用本文复制引用
廖旭..Sylvester连分数展式中若干例外集的Hausdorff维数[J].数学杂志,2024,44(4):343-357,15.基金项目
重庆市教育委员会科学技术研究项目资助(KJQN202100528) （KJQN202100528）
重庆市自然科学基金资助(CSTB2022NSCQ-MSX1255). （CSTB2022NSCQ-MSX1255）
