Algebraic and ergodic properties of a new continued fraction algorithm with non-decreasing partial quotients
Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 497-516.

On introduit la notion de développement en fractions continues de Engel. Nous étudions notamment les propriétés ergodiques de ce développement et le lien avec celui introduit par F. Ryde monotonen, nicht-abnehmenden Kettenbruch.

In this paper the Engel continued fraction (ECF) expansion of any x∈(0,1) is introduced. Basic and ergodic properties of this expansion are studied. Also the relation between the ECF and F. Ryde’s monotonen, nicht-abnehmenden Kettenbruch (MNK) is studied.

@article{JTNB_2002__14_2_497_0,
     author = {Hartono, Yusuf and Kraaikamp, Cor and Schweiger, Fritz},
     title = {Algebraic and ergodic properties of a new continued fraction algorithm with non-decreasing partial quotients},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {497--516},
     publisher = {Universit\'e Bordeaux I},
     volume = {14},
     number = {2},
     year = {2002},
     mrnumber = {2040690},
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Hartono, Yusuf; Kraaikamp, Cor; Schweiger, Fritz. Algebraic and ergodic properties of a new continued fraction algorithm with non-decreasing partial quotients. Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 497-516. https://www.numdam.org/item/JTNB_2002__14_2_497_0/

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