Density of expansivity for geodesic flows of compact higher genus surfaces without conjugate points

2024/09/24 by Mamani, Edhin F., Ruggiero, Rafael
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.15768

Abstract

Let (M,g) be a compact connected C^∞ surface without conjugate points of genus greater than one. We show that set of geodesics without strips forms a dense set of orbits in the unit tangent bundle. This fact was known assuming no focal points as a consequence of a result of Coudène and Shapira. They showed that flat strips are periodic and hence form a set of zero measure in the unit tangent bundle.

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