Distribution of periodic points of certain Gauss shifts with infinite invariant measure

Florin P. Boca, Maria Siskaki

Research output: Contribution to journalArticlepeer-review

Abstract

This paper investigates the periodic points of the Gauss type shifts associated to the even continued fraction (Schweiger) and to the backward continued fraction (Rényi). We show that they coincide exactly with two sets of quadratic irrationals that we call E-reduced, and respectively B-reduced. We prove that these numbers are equidistributed with respect to the (infinite) Lebesgue absolutely continuous invariant measures of the corresponding Gauss shift.

Original languageEnglish (US)
Pages (from-to)4570-4603
Number of pages34
JournalNonlinearity
Volume34
Issue number7
DOIs
StatePublished - Jul 2021

Keywords

  • backward continued fraction
  • equidistribution
  • even continued fraction
  • Gauss shift
  • Pell equation
  • periodic points

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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