Variations on the real projective orbits of \(\text{SL}(2,\mathbb Z)\) and \(\text{GL}(2,\mathbb Z)\) (Q1611554)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Variations on the real projective orbits of \(\text{SL}(2,\mathbb Z)\) and \(\text{GL}(2,\mathbb Z)\) |
scientific article; zbMATH DE number 1786582
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Variations on the real projective orbits of \(\text{SL}(2,\mathbb Z)\) and \(\text{GL}(2,\mathbb Z)\) |
scientific article; zbMATH DE number 1786582 |
Statements
Variations on the real projective orbits of \(\text{SL}(2,\mathbb Z)\) and \(\text{GL}(2,\mathbb Z)\) (English)
0 references
24 August 2003
0 references
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.
0 references
linear groups
0 references
projective line
0 references
continued fractions
0 references
Fermat-Pell equations
0 references
