A Closing Lemma for Non-uniformly Hyperbolic Singular Flows

In this paper, we combine the profound Pesin theory with the sophisticated approach for addressing singular flows devised by Liao and prove a closing lemma for \(C^{1+\alpha }\) $C^{1+\alpha }$ non-uniform hyperbolic singular flows. As an application, we prove that every ergodic hyperbolic measure which is not supported on singularities can be approximated by periodic measures.