论文标题
在半规则的持续分数中具有受限制，缓慢增长的部分代价的套装尺寸
Hausdorff dimension of sets with restricted, slowly growing partial quotients in semi-regular continued fractions
论文作者
论文摘要
我们确定$（0,1）$中非理性的豪斯多夫维度，其半定期持续分数中的部分商遵守某些限制和增长条件。该结果大大概括了第二作者的[Proc。阿米尔。数学。 Soc。 {\ bf 151}（2023），3645--3653]和赫斯特猜想的解决方案[B.-W。 Wang和J. Wu，公牛。伦敦数学。 Soc。 {\ bf 40}（2008），18--22]，均以常规持续分数获得。为了证明结果，我们构建了针对给定限制和生长条件的非自主迭代功能系统，估计相关的压力功能，然后应用Bowen的公式。
We determine the Hausdorff dimension of sets of irrationals in $(0,1)$ whose partial quotients in semi-regular continued fractions obey certain restrictions and growth conditions. This result substantially generalizes that of the second author [Proc. Amer. Math. Soc. {\bf 151} (2023), 3645--3653] and the solution of Hirst's conjecture [B.-W. Wang and J. Wu, Bull. London Math. Soc. {\bf 40} (2008), 18--22], both previously obtained for the regular continued fraction. To prove the result, we construct non-autonomous iterated function systems well-adapted to the given restrictions and growth conditions on partial quotients, estimate the associated pressure functions, and then apply Bowen's formula.
