Print Email Facebook Twitter Invariant measures for continued fraction algorithms with finitely many digits Title Invariant measures for continued fraction algorithms with finitely many digits Author Kraaikamp, C. (TU Delft Applied Probability) Langeveld, Niels (Universiteit Leiden) Date 2017-10 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. Subject Continued fraction expansionsEntropyGauss–Kuzmin–LévyInvariant measureNatural extension To reference this document use: http://resolver.tudelft.nl/uuid:f2bc19c9-f158-4374-b059-bf0dc32ef7b6 DOI https://doi.org/10.1016/j.jmaa.2017.04.067 Embargo date 2019-05-15 ISSN 0022-247X Source Journal of Mathematical Analysis and Applications, 454 (1), 106-126 Bibliographical note Author Accepted Manuscript Part of collection Institutional Repository Document type journal article Rights © 2017 C. Kraaikamp, Niels Langeveld Files PDF articlegausskuzminelsFINAL.pdf 626.06 KB Close viewer /islandora/object/uuid:f2bc19c9-f158-4374-b059-bf0dc32ef7b6/datastream/OBJ/view