An elegant model of the geodesic flow on the modular surface
Abstract
Caroline Series' [{\em The modular surface and continued fractions}, J. Lond. Math. Soc. (2), {\bf 31}, no.~1, (1985), 69--80] gives a clear framework linking, in a deceptively simple way, the dynamics of the geodesic flow on the modular surface with the dynamics of the regular continued fraction, through a well-chosen symbolic coding. It has been called {\em required reading} for those interested in the symbolic dynamics of geodesic flows, and has had consequences in symbolic dynamics, ergodic theory, hyperbolic geometry, and continued fraction theory. In this overview, we give an indication of why this is so, sketch some of the history related to the paper, and also point to some later works.
Cite
@article{arxiv.2605.09230,
title = {An elegant model of the geodesic flow on the modular surface},
author = {Pierre Arnoux and Thomas A. Schmidt},
journal= {arXiv preprint arXiv:2605.09230},
year = {2026}
}
Comments
18 pages, 4 figures, to appear in the centenary issue of the JLMS