On Arnoux's coding of the geodesic flow on the modular surface.

Speaker: Thomas A. Schmidt, Oregon State University

Date: Wed, Oct 25, 2023

Location: Online, University of Utah

Conference: University of Utah Seminar in Ergodic Theory

Subject: Mathematics

Class: Scientific


I will present Pierre Arnoux's 1994 paper in which he applies Veech's notion of zippered rectangles in the genus one setting to coordinatize the unit tangent bundle of the modular surface and thereby win an explicit description of its geodesic flow. From this, Arnoux recovered a result of C. Series': the dynamical system defined by the Gauss map (underlying regular continued fractions) is a factor of a section to the geodesic flow on the aforementioned unit tangent bundle. Time permitting, I will sketch some further implications given in the paper.