Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology

2014/12/10 by Fernando Alcalde Cuesta, Françoise Dal’Bo, Alcalde, Fernando +5 · 1 citation
Mathematics · #37A17 #37D40 #58J65 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1412.3259

openalex publication_date 2014/12/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider a minimal compact lamination by hyperbolic surfaces. We prove that if it admits a leaf whose holonomy covering is not topologically trivial, then the horocycle flow on its unitary tangent bundle is minimal.

Citations

• REMARKS ON THE DYNAMICS OF THE HOROCYCLE FLOW FOR HOMOGENEOUS FOLIATIONS BY HYPERBOLIC SURFACES

Cited by

• Recurrent and irregular orbits of the horocyclic flow on the unit tangent bundle of the untwisted flute

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• Remarks on the horocycle flows for foliations by hyperbolic surfaces
• Horocycle flows without minimal sets
• Topology of leaves for minimal laminations by non-simply connected hyperbolic surfaces
• Topology of leaves for minimal laminations by hyperbolic surfaces