Abstract: I will describe a new Poincaré map P_h for the horocycle flow on the modular surface. The map P_h is defined on a section used to define a Poincaré map for the geodesic flow, and in this way both maps turn out to be related to the Stern-Brocot tree of positive rational numbers. This is a classical result for the geodesic flow, but to my knowledge this is the first example of such a connection for the horocycle flow. I will show some of the dynamical properties of the map P_h which can be proved independently from known results for the horocycle flow.
This is based on joint work with A. Del Vigna and S. Isola.
Flows on the modular surface and trees of fractions
14.07.2022 15:15 - 16:15
Organiser:
D. Ravotti
Location: