Weaving Geodesics and New Phenomena in Horocyclic Dynamics
Dynamical Systems
2026-02-26 v3 Geometric Topology
Abstract
We construct geometrically infinite hyperbolic surfaces supporting horocycles with tailored recurrence properties. In particular, we obtain the first examples of non-trivial minimal horocyclic orbit closures and of infinite locally-finite conservative horocyclic invariant measures which are singular with respect to the geodesic flow. Other examples include surfaces supporting horocyclic orbit closures of arbitrary Hausdorff dimension in .
Cite
@article{arxiv.2510.24609,
title = {Weaving Geodesics and New Phenomena in Horocyclic Dynamics},
author = {Françoise Dal'bo and James Farre and Or Landesberg and Yair Minsky},
journal= {arXiv preprint arXiv:2510.24609},
year = {2026}
}
Comments
21 pages, 4 figures, rewritten subsection 1.5 and section 2 for improved readability - results unchanged