Ergodic Geodesic Flows and First Kind Flute Surfaces

2025/10/28 by Gordillo, Erick, Quellec, Nolwenn Le
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2510.24576

Abstract

We study flute surfaces and extend results of Pandazis and Šarić giving necessary and sufficient conditions on the Fenchel-Nielsen coordinates of the surface to be of the first kind. As a consequence of the first result, we characterize parabolic flute surfaces (i.e. flute surfaces with ergodic geodesic flow) with twist parameters in 0,1/2, extending the work of Pandazis and Šarić.

Citations

• Inducing recurrent flows by twisting on infinite surfaces with unbounded cuffs
• Non-ergodicity of the geodesic flow on Cantor tree surfaces
• Ergodicity of the geodesic flow on symmetric surfaces
• Quadratic differentials and foliations on infinite Riemann surfaces
• The type problem for Riemann surfaces via Fenchel-Nielsen parameters

Related

• Ergodicity of the geodesic flow on symmetric surfaces
• The type problem for Riemann surfaces via Fenchel-Nielsen parameters
• Recurrent and irregular orbits of the horocyclic flow on the unit tangent bundle of the untwisted flute
• Inducing recurrent flows by twisting on infinite surfaces with unbounded cuffs
• Non-ergodicity of the geodesic flow on Cantor tree surfaces