Some Dynamical Properties on Manifolds with no Conjugate Points

Fei Liu, Xiaokai Liu, Fang Wang

Published 2021-05-15, updated 2021-08-16Version 2

In this article, we study the dynamics of geodesic flows on Riemannian (not necessarily compact) manifolds with no conjugate points. We prove the Anosov Closing Lemma, the local product structure, and the transitivity of the geodesic flows on $\Omega_1$ under the conditions of bounded asymptote and uniform visibility. As an application, we further discuss about some generic properties of the set of invariant probability measures