The mother of all continued fractions
The mother of all continued fractions
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所有连分数之母
DOI：
10.4064/cm-84/85-1-109-123
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
C. Kraaikamp
中科院分区：
文献类型：
--
作者：
K. Dajani;C. Kraaikamp
在本文中，我们使用称为插入的过程给出正则连分数和 Lehner 分数之间的关系。从任何实无理数 x 的正则连分式展开开始，当应用最大插入次数时，可以获得 x 的 Lehner 分数。插入和奇异化显示了这些和其他连分式展开如何相关。我们还将研究 Lehner 分数和 Farey 展开之间的关系，并获得 Farey 展开基础的各态遍历系统
In this paper we give the relationship between the regular continued fraction and the Lehner fractions using a procedure known as insertion Starting from the regular continued fraction expansion of any real irrational x when the maximal number of insertions is applied one obtains the Lehner fraction of x Insertions and singularizations show how these and other continued fractions expansions are related We will also investigate the relation between the Lehner fractions and the Farey expansion and obtain the ergodic system underlying the Farey expansion