Bellis strong stable sets on infinite hyperbolic surfaces
Dynamical Systems
2026-04-06 v1
Abstract
We provide a corrected proof of a theorem of A. Bellis on strong stable sets in the unit tangent bundle of certain hyperbolic surfaces. The theorem states that, for vectors whose geodesic rays encounter arbitrarily short closed geodesics, the strong stable set in the dynamical sense does not coincide with the associated horocyclic orbit. The proof is based on Bellis' idea of constructing geodesic rays that wind around infinitely many closed geodesics.
Cite
@article{arxiv.2604.02649,
title = {Bellis strong stable sets on infinite hyperbolic surfaces},
author = {Sergi Burniol Clotet and Françoise Dal'Bo and Sergio Herrero Vila},
journal= {arXiv preprint arXiv:2604.02649},
year = {2026}
}
Comments
13 pages, 2 figures