ALTERNATING N-EXPANSIONS

Publikationen: Beitrag in FachzeitschriftArtikelForschung(peer-reviewed)

Autoren

Externe Organisationseinheiten

  • Universität Utrecht

Abstract

We introduce a family of maps generating continued fractions where the digit 1 in the numerator is replaced cyclically by some given non-negative integers (N_1, . . . , N_m). We prove the convergence of the given algorithm, and study the underlying dynamical system generating such expansions. We prove the existence of a unique absolutely continuous invariant ergodic measure. In special cases, we are able to build the natural extension and give an explicit expression of the invariant measure. For these cases, we formulate a Doeblin-Lenstra type theorem. For other cases we have a more implicit expression that we conjecture gives the invariant density. This conjecture is supported by simulations. For the simulations we use a method that gives us a smooth approximation in every iteration.

Details

OriginalspracheEnglisch
AufsatznummerA65
Seitenumfang25
FachzeitschriftINTEGERS: Electronic Journal of Combinatorial Number Theory
Jahrgang2022
Ausgabenummer22
StatusVeröffentlicht - 7 Aug. 2022