标题： 高斯映射的豪斯多夫测度的渐近性及其线性化类比 显示英文标题

标题： Asymptotics of the Hausdorff measure for the Gauss map and its linearized analogue

摘要： 对于$n\in\mathbb N$，我们考虑区间 [0,1] 内点的集合$J_n$，这些点的连分数展开项被 n 限制。类似地，我们考虑集合$J_n$，它是高斯映射的线性化类比。 我们研究了集合$J_n$的 Hausdorff 测度的渐近性质（在其 Hausdorff 维数下评估）。 我们得到了线性化高斯映射的精确渐近性质，并且对于原始高斯映射的渐近性质也得到了相同的单侧界。 显示英文摘要

摘要： For $n\in\mathbb N$ we consider the set $J_n$ of points in the interval [0,1] whose continued fraction expansion entries are bounded by n. Similarly, we consider the set $J_n$ for the linearized analogue of the Gauss map. We study the asymptotic of the Hausdorff measure of the set $J_n$, (evaluated at its Hausdorff dimension). We obtain precise asymptotics for the linearized Gauss map and the same one -sided bound for the asymptotics for the original Gauss map.