论文标题
通过熵比较不同持续分数算法的效率的湖泊型方法
A Lochs-Type Approach via Entropy in Comparing the Efficiency of Different Continued Fraction Algorithms
论文作者
论文摘要
我们利用1964年的湖泊定理的概括研究了单位间隔中数字的几种类型的持续分数扩展的效率。因此，我们旨在通过描述一个数字理论扩展的数字确定另一个数字的数字来比较效率。我们研究Chan的持续分数，$θ$ - 扩展，$ n $ - 连接的分数和rényi-type持续分数。实现我们目标的核心作用是由相关动力学系统绝对连续不变的概率度量的熵发挥的。
We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964. Thus, we aimed to compare the efficiency by describing the rate at which the digits of one number-theoretic expansion determine those of another. We study Chan's continued fractions, $θ$-expansions, $N$-continued fractions and Rényi-type continued fractions. A central role in fulfilling our goal is played by the entropy of the absolutely continuous invariant probability measures of the associated dynamical systems.
