Log In

Ergodicityof N-continuedfractionexpansions

Files

How and where to find an Open Access version of this publication?

Publication date

2013-09

Authors

Dajani, K.ISNI 0000000117632256
Kraaikamp, C.
van der Wekken, N.

Editors

Advisors

Supervisors

DOI

https://doi.org/10.1016/j.jnt.2013.02.017

Document Type

Article

Metadata

Show full item record

Collections

Utrecht University Repository

License

Abstract

Recently,EdwardBurgerandhisco-authorsintroducedandstudied in Burgeretal.(2008) [3] a newclassofcontinuedfraction algorithms.Inparticulartheyshowedthatforeveryquadratic irrationalnumber x thereexistinfinitelymanyeventuallyperiodic N-expansionswithperiod-length1;seealsoKomatsu(2009) [10] forrelatedproperties.In2011,MaxwellAnselmandSteven Weintraubfurtherstudiedthepropertiesof N-expansionsin Anselm andWeintraub(2011) [2]. Oneniceresulttheyobtainedis that every x between0and N has uncountablymany N-expansions for eachinteger N 2. Inthispaperwewillreprovethisresultand fromthiswestudytheergodicpropertiesofvarioussubclassesof N-expansions.

Keywords

Continued fractions, Ergodicity, σ-Finite, infinite invariant measure

Citation

Dajani, K, Kraaikamp, C & van der Wekken, N 2013, 'Ergodicityof N-continuedfractionexpansions', Journal of Number Theory, vol. 133, no. 9, pp. 3183-3204. https://doi.org/10.1016/j.jnt.2013.02.017

URI

https://dspace.library.uu.nl/handle/1874/290262