Closed geodesics in dilation surfaces
Geometric Topology
2024-07-15 v3 Dynamical Systems
Abstract
We prove that directions of closed geodesics in every dilation surface form a dense subset of the circle. The proof draws on a study of the degenerations of the Delaunay triangulation of dilation surfaces under the action of Teichm\"{u}ller flow in the moduli space.
Cite
@article{arxiv.2110.06061,
title = {Closed geodesics in dilation surfaces},
author = {Adrien Boulanger and Selim Ghazouani and Guillaume Tahar},
journal= {arXiv preprint arXiv:2110.06061},
year = {2024}
}
Comments
31 pages, 16 figures