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arXiv · 2510.24609

Weaving Geodesics and New Phenomena in Horocyclic Dynamics

Françoise Dal'bo·James Farre·Or Landesberg·Yair Minsky
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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 $(1,2)$.

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Françoise Dal'bo, James Farre, Or Landesberg, Yair Minsky. 2025-10-28. Weaving Geodesics and New Phenomena in Horocyclic Dynamics. https://arxiv.org/abs/2510.24609

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