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math.DS2023★ 1 cited
The Hopf-Tsuji-Sullivan Dichotomy on Visibility Manifolds Without Conjugate Points
Fei Liu, Xiaokai Liu, Fang Wang
In this article, we establish the Hopf-Tsuji-Sullivan dichotomy for geodesic flows on certain manifolds with no conjugate points: either the geodesic flow is conservative and ergod…
math.DS2021
Some Dynamical Properties on Manifolds with no Conjugate Points
Fei Liu, Xiaokai Liu, Fang Wang
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 pr…
math.DS2018
On the mixing and Bernoulli properties for geodesic flows on rank 1 manifolds without focal points
Fei Liu, Xiaokai Liu, Fang Wang
If is a smooth compact rank Riemannian manifold without focal points, it is shown that the measure of maximal entropy for the geodesic flow is unique. In thi…