论文标题
定量失真和持续分数的Hausdorff尺寸
Quantitative distortion and the Hausdorff dimension of continued fractions
论文作者
论文摘要
我们证明了迭代函数系统的定量失真定理，该系统生成了一组持续的分数。结果，我们在任何一组实际或复杂的持续分数的豪斯多夫尺寸上获得了上限和下限。这些界限是可以在计算机代数系统中轻松实现的汇聚中moran型方程的解决方案。
We prove a quantitative distortion theorem for iterated function systems that generate sets of continued fractions. As a consequence, we obtain upper and lower bounds on the Hausdorff dimension of any set of real or complex continued fractions. These bounds are solutions to Moran-type equations in the convergents that can be easily implemented in a computer algebra system.
