`THE MOTHER OF ALL CONTINUED FRACTIONS' KARMA DAJANI AND COR KRAAIKAMP
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Abstract:
Dedicated to the memory of Anzelm Iwanik Abstract. 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.
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