论文标题
某些持续分数的尺寸，不折衷的部分商
Dimensions of certain sets of continued fractions with non-decreasing partial quotients
论文作者
论文摘要
令$ [a_1（x），a_2（x），a_3（x），\ cdots] $为$ x \ in（0,1）$的持续分数扩展。本文关注的是一组持续的分数，而偏重的部分代理。作为主要结果，我们获得了集合\ [\ left \ {x \ in（0,1）的豪斯多夫维度对于任何$ψ：\ mathbb {n} \ rightArrow \ Mathbb {r}^+$满足$ n \ infty $ n \ infty unfty $。
Let $[a_1(x),a_2(x),a_3(x),\cdots]$ be the continued fraction expansion of $x\in (0,1)$. This paper is concerned with certain sets of continued fractions with non-decreasing partial quotients. As a main result, we obtain the Hausdorff dimension of the set \[\left\{x\in(0,1): a_1(x)\leq a_2(x)\leq \cdots,\ \limsup\limits_{n\to\infty}\frac{\log a_n(x)}{ψ(n)}=1\right\}\] for any $ψ:\mathbb{N}\rightarrow\mathbb{R}^+$ satisfying $ψ(n)\to\infty$ as $n\to\infty$.
