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<p>In this article, we study the hyperbolic dynamics of geodesic flows on Riemannian (not necessarily compact) manifolds with no conjugate points. By hyperbolic dynamics, we focus on the Anosov Closing Lemma, the local product structure, and the transitivity of the geodesic flows on the set of rank 1 non-wandering set Ω<sub>1</sub> under the conditions of bounded asymptote and uniform visibility. As an application, we further discuss on some generic properties of the set of invariant probability measures.</p>

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Hyperbolic Properties of Geodesic Flows on Certain Manifolds without Conjugate Points

  • 期刊论文

  • 发表日期：

    2025年10月15日

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  • Fei Liu,
  • Xiaokai Liu,
  • Fang Wang

摘要

In this article, we study the hyperbolic dynamics of geodesic flows on Riemannian (not necessarily compact) manifolds with no conjugate points. By hyperbolic dynamics, we focus on the Anosov Closing Lemma, the local product structure, and the transitivity of the geodesic flows on the set of rank 1 non-wandering set Ω1 under the conditions of bounded asymptote and uniform visibility. As an application, we further discuss on some generic properties of the set of invariant probability measures.