'The mother of all continued fractions'
Dajani, Karma ; Kraaikamp, Cor
Colloquium Mathematicae, Tome 84/85 (2000), p. 109-123 / Harvested from The Polish Digital Mathematics Library
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We give the relationship between regular continued fractions and 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 fraction expansions are related. We also investigate the relation between Lehner fractions and the Farey expansion (also known as the full continued fraction), and obtain the ergodic system underlying the Farey expansion.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:210790 
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     title = {'The mother of all continued fractions'},
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     year = {2000},
     pages = {109-123},
     zbl = {0961.11027},
     language = {en},
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Dajani, Karma; Kraaikamp, Cor. 'The mother of all continued fractions'. Colloquium Mathematicae, Tome 84/85 (2000) pp. 109-123. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv84i1p109bwm/

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