Robust transitivity of geodesic flows from metrics with conjugate points

Ygor de Jesus; Luis Pedro Piñeyrúa; Sergio Romaña

Robust transitivity of geodesic flows from metrics with conjugate points

Dynamical Systems 2026-07-03 v1 Differential Geometry General Topology

Authors: Ygor de Jesus , Luis Pedro Piñeyrúa , Sergio Romaña

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 $C^2$ 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.

Keywords

geodesic flows robust transitivity partially hyperbolic conjugate points Riemannian metrics Anosov flows

Cite

@article{arxiv.2607.03319,
  title  = {Robust transitivity of geodesic flows from metrics with conjugate points},
  author = {Ygor de Jesus and Luis Pedro Piñeyrúa and Sergio Romaña},
  journal= {arXiv preprint arXiv:2607.03319},
  year   = {2026}
}

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24 pages