Geodesic
'The mother of all continued fractions'
Colloquium Mathematicum, Tome 84 (2000) no. 1, pp. 109-123.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm-84/85-1-109-123
Keywords: insertion, ergodic theory, continued fractions, singularization

Karma Dajani 1 ; Cor Kraaikamp 1

1 
@article{10_4064_cm_84_85_1_109_123,
     author = {Karma Dajani and Cor Kraaikamp},
     title = {'The mother of all continued fractions'},
     journal = {Colloquium Mathematicum},
     pages = {109--123},
     publisher = {mathdoc},
     volume = {84},
     number = {1},
     year = {2000},
     doi = {10.4064/cm-84/85-1-109-123},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-84/85-1-109-123/}
}
TY  - JOUR
AU  - Karma Dajani
AU  - Cor Kraaikamp
TI  - 'The mother of all continued fractions'
JO  - Colloquium Mathematicum
PY  - 2000
SP  - 109
EP  - 123
VL  - 84
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm-84/85-1-109-123/
DO  - 10.4064/cm-84/85-1-109-123
LA  - en
ID  - 10_4064_cm_84_85_1_109_123
ER  - 
%0 Journal Article
%A Karma Dajani
%A Cor Kraaikamp
%T 'The mother of all continued fractions'
%J Colloquium Mathematicum
%D 2000
%P 109-123
%V 84
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm-84/85-1-109-123/
%R 10.4064/cm-84/85-1-109-123
%G en
%F 10_4064_cm_84_85_1_109_123
Karma Dajani; Cor Kraaikamp. 'The mother of all continued fractions'. Colloquium Mathematicum, Tome 84 (2000) no. 1, pp. 109-123. doi : 10.4064/cm-84/85-1-109-123. http://geodesic.mathdoc.fr/articles/10.4064/cm-84/85-1-109-123/

Cité par Sources :