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 language | English (US) |
|---|---|
| Pages (from-to) | 4570-4603 |
| Number of pages | 34 |
| Journal | Nonlinearity |
| Volume | 34 |
| Issue number | 7 |
| DOIs | |
| State | Published - Jul 2021 |
Keywords
- Gauss shift
- Pell equation
- backward continued fraction
- equidistribution
- even continued fraction
- periodic points
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics