Continued fraction expansions with variable numerators

K. Dajani, Cor Kraaikamp, Niels Langeveld

Research output: Contribution to journalArticleAcademicpeer-review


A new continued fraction expansion algorithm, the so-called -expansion, is introduced and some of its basic properties, such as convergence of the algorithm and ergodicity of the underlying dynamical system, have been obtained. Although seemingly a minor variation of the regular continued fraction (RCF) expansion and its many variants (such as Nakada's -expansions, Schweiger's odd- and even-continued fraction expansions, and the Rosen fractions), these -expansions behave very differently from the RCF and many important question remains open, such as the exact form of the invariant measure, and the "shape" of the natural extension.
Original languageEnglish
Pages (from-to)617–639
Number of pages22
JournalThe Ramanujan Journal
Issue number3
Publication statusPublished - 2015


  • Continued fractions
  • Ergodicity
  • Invariant measures


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