Robust transitivity of geodesic flows from metrics with conjugate points

2026/07/03 by Ygor de Jesus, Luis Pedro Piñeyrúa, Sergio Romaña
#math.DS #math.DG #math.GN

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Abstract

In this article, we prove a general criterion for obtaining robust transitivity of partially hyperbolic geodesic flows. As a consequence, we exhibit the first example of a C² open set of Riemannian metrics with conjugate points and transitive geodesic flow. In particular, such a set does not intersect the set of Riemannian metrics with Anosov geodesic flows.

Related

• Partially hyperbolic geodesic flow via conformal deformation
• Geodesic Anosov flows, hyperbolic closed geodesics and stable ergodicity
• Some Dynamical Properties on Manifolds with no Conjugate Points
• Riemannian manifolds with Anosov geodesic flow do not have conjugate points
• Partially hyperbolic geodesic flows