Variations on the real projective orbits of \(\text{SL}(2,\mathbb Z)\) and \(\text{GL}(2,\mathbb Z)\)
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.
scientific article; zbMATH DE number 1786582