Variations on the real projective orbits of \(\text{SL}(2,\mathbb Z)\) and \(\text{GL}(2,\mathbb Z)\)
type: Item
instance of: scholarly article
title: Variations on the real projective orbits of \(\text{SL}(2,\mathbb Z)\) and \(\text{GL}(2,\mathbb Z)\)
zbMATH Open document ID: 1022.11018
DOI: 10.1016/S0723-0869(02)80018-4
author: Jean-Louis Cathelineau
published in: Expositiones Mathematicae
publication date: 2003-08-24T00:00:00Z
review text: The author provides a very readable, elementary article on the action of \(\text{GL}(2,\mathbb Z)\) by homographies on the projective line \(\mathbb P^1(\mathbb R)=\mathbb R\cup\{\infty\}\). This includes a comparison of the orbits of \(\text{GL}(2,\mathbb Z)\) and \(\text{SL} (2,\mathbb Z)\), which provides new connections with continued fractions and Fermat-Pell equations. This is recommended reading.
Mathematics Subject Classification ID: 11F06
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 11D09
zbMATH DE Number: 1786582
zbMATH Keywords: linear groups
zbMATH Keywords: projective line
zbMATH Keywords: continued fractions
zbMATH Keywords: Fermat-Pell equations
reviewed by: Richard A. Mollin
MaRDI profile type: Publication
cites work: Simple continued fraction solutions for Diophantine equations
cites work: Q4417777
cites work: Q3337526
cites work: Q5596313
description: scientific article; zbMATH DE number 1786582