'The mother of all continued fractions'

• Autorzy: Karma Dajani , Cor Kraaikamp
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

insertion; ergodic theory; continued fractions; singularization

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2000
• Tom: 84/85
• Numer: 1
• Strony: 109-123

Daty

wydano

2000

otrzymano

1999-05-25

poprawiono

1999-09-22

Twórcy

autor

Karma Dajani

• Universiteit Utrecht, Fac. Wiskunde en Informatica and MRI, Budapestlaan 6, P.O. Box 80.000, 3508 TA Utrecht, the Netherlands

autor

Cor Kraaikamp

• Technische Universiteit Delft, ITS (SSOR) Thomas Stieltjes Institute for Mathematics, Mekelweg 4, 2628 CD Delft, the Netherlands

Bibliografia

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