Conjugacies of geodesic flows in affine cylinders and tori
Dynamical Systems
2025-09-09 v1
Abstract
Affine cylinders (genus zero surfaces with two singularities) and affine tori (genus one surfaces without singularities) are among the simplest examples of surfaces endowed with a complex affine structure. Their geodesic flows are particularly tractable. In this article, we provide explicit necessary and sufficient conditions under which the geodesic flows on such surfaces are conjugate, in the topological and in the holomorphic category.
Keywords
Cite
@article{arxiv.2509.06391,
title = {Conjugacies of geodesic flows in affine cylinders and tori},
author = {Xavier Buff and Guillaume Tahar},
journal= {arXiv preprint arXiv:2509.06391},
year = {2025}
}