A Poincaré map for the horocycle flow on $PSL(2,\mathbb{Z})\backslash \mathbb{H}$ and the Stern-Brocot tree

Claudio Bonanno, Alessio Del Vigna, Stefano Isola

We construct a Poincaré map ${\mathcal{P}}_h$ for the positive horocycle flow on the modular surface $PSL(2,\mathbb{Z})\backslash \mathbb{H}$, and begin a systematic study of its dyn…