Closed geodesics in dilation surfaces

2021/10/12 by Adrien Boulanger, Boulanger, Adrien, Selim Ghazouani +3 · 1 citation
Earth and Planetary Sciences · #Dynamical Systems (math.DS) #FOS: Mathematics #Geological Modeling and Analysis #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.2110.06061

openalex publication_date 2021/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that directions of closed geodesics in every dilation surface form a dense subset of the circle. The proof draws on a study of the degenerations of the Delaunay triangulation of dilation surfaces under the action of Teichmüller flow in the moduli space.

Cited by

• Invariant measures on moduli spaces of twisted holomorphic 1-forms and strata of dilation surfaces

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