Minimizing laminations in regular covers, horospherical orbit closures, and circle-valued Lipschitz maps

2023/06/25 by James Farre, Farre, James, Or Landesberg +3 · 1 citation
Mathematics · #22F30 #30F60 #37B20 #37B99 (Secondary) #37D40 #57K20 (Primary) 37A17 #57K32 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2306.14296

openalex publication_date 2023/06/25 · openalex created_date 2023/06/28 · openalex updated_date 2026/07/28

Abstract

We expose a connection between distance minimizing laminations and horospherical orbit closures in ℤ-covers of compact hyperbolic manifolds. For surfaces, we provide novel constructions of ℤ-covers with prescribed geometric and dynamical properties, in which an explicit description of all horocycle orbit closures is given. We further show that even the slightest of perturbations to the hyperbolic metric on a ℤ-cover can lead to drastic topological changes to horocycle orbit closures.

Cited by

• Weaving Geodesics and New Phenomena in Horocyclic Dynamics

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