## Abstract

In this paper we consider continued fraction (CF) expansions on intervals different from [0,1]. For every x in such interval we find a CF expansion with a finite number of possible digits. Using the natural extension, the density of the invariant measure is obtained in a number of examples. In case this method does not work, a Gauss–Kuzmin–Lévy based approximation method is used. Convergence of this method follows from [32] but the speed of convergence remains unknown. For a lot of known densities the method gives a very good approximation in a low number of iterations. Finally, a subfamily of the N-expansions is studied. In particular, the entropy as a function of a parameter α is estimated for N=2 and N=36. Interesting behavior can be observed from numerical results.

Original language | English |
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Pages (from-to) | 106-126 |

Number of pages | 21 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 454 |

Issue number | 1 |

DOIs | |

Publication status | Published - Oct 2017 |

### Bibliographical note

Author Accepted Manuscript## Keywords

- Continued fraction expansions
- Entropy
- Gauss–Kuzmin–Lévy
- Invariant measure
- Natural extension