$ \mathbb{Z} $ 覆盖中的角循环轨道闭合分类

arXiv - MATH - Geometric Topology Pub Date : 2024-09-16 DOI:arxiv-2409.10004

James Farre, Or Landesberg, Yair Minsky

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引用次数: 0

摘要

我们完全描述了紧凑双曲面的$ \mathbb{Z} $覆盖中的所有角循环轨道闭合。我们的结果依赖于对覆盖中所有距离最小化大地射线效率的仔细分析。作为必然结果，我们得到了在这种情况下，所有非最大角循环轨道闭合虽然都是分形的，但其豪斯多夫维度都是整数。

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Classification of horocycle orbit closures in $ \mathbb{Z} $-covers

We fully describe all horocycle orbit closures in $ \mathbb{Z} $-covers of compact hyperbolic surfaces. Our results rely on a careful analysis of the efficiency of all distance minimizing geodesic rays in the cover. As a corollary we obtain in this setting that all non-maximal horocycle orbit closures, while fractal, have integer Hausdorff dimension.

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arXiv - MATH - Geometric Topology

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