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Some Dynamical Properties on Manifolds with no Conjugate Points

Authors :
Liu, Fei
Liu, Xiaokai
Wang, Fang
Publication Year :
2021

Abstract

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<br />Comment: 38 pages, 14 figures, update references and correct a few typos

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2105.07170
Document Type :
Working Paper