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

作　　者：廖旭 LIAO Xu(Chongqing Normal University(School of Mathematical Sciences),Chongqin 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《数学杂志》2024年第4期343-357,共15页Journal of Mathematics

基　　金：重庆市教育委员会科学技术研究项目资助(KJQN202100528);重庆市自然科学基金资助(CSTB2022NSCQ-MSX1255)。

摘　　要：对于任意实数x∈(0,1],记x=[d_(1),d_(2),···]为x的Sylvester连分数展式,令ψ(n)为N上的正函数,本文研究了集合A(ψ):■的Hausdorff维数.通过构造覆盖和合适的Cantor型子集,我们得到了该集合的精确维数为■同时,本文还考虑了Sylvester连分数展式的部分商满足■的极限是零或无穷时的集合的Hausdorff维数.For x∈(0,1],let x=[d_(1),d_(2),···]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)=■;whereψ(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 dimH A(ψ)=■:At the same time,we also calculate the Hausdorff dimension of the set of points with■.

关 键 词：Sylvester连分数 HAUSDORFF维数 增长速度 

分 类 号：O156.7[理学—数学]