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Weaving Geodesics and New Phenomena in Horocyclic Dynamics (2510.24609v1)
Published 28 Oct 2025 in math.DS and math.GT
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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