| Title: |
Inducing contractions of the mother of all continued fractions |
| Authors: |
Dajani, Karma; Kraaikamp, Cor; Sanderson, Slade; Sub Mathematical Modeling; Mathematical Modeling |
| Publication Year: |
2026 |
| Subject Terms: |
Continued fractions; Contraction; Ergodic theory; Induced transformation; Natural extension; Algebra and Number Theory |
| Description: |
We introduce a new, large class of continued fraction algorithms producing what are called contracted Farey expansions. These algorithms are defined by coupling two acceleration techniques—induced transformations and contraction—in the setting of Shunji Ito's ([19]) natural extension of the Farey tent map, which generates ‘slow’ continued fraction expansions. In addition to defining new algorithms, we also realise several existing continued fraction algorithms in our unifying setting. In particular, we find regular continued fractions, the second-named author's S-expansions, and Nakada's parameterised family of α-continued fractions for all 0 |
| Document Type: |
article in journal/newspaper |
| File Description: |
application/pdf |
| Language: |
English |
| ISSN: |
0022-314X |
| Relation: |
https://dspace.library.uu.nl/handle/1874/478026 |
| Availability: |
https://dspace.library.uu.nl/handle/1874/478026 |
| Rights: |
info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.95885F2A |
| Database: |
BASE |