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 C1+alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C<<^>>{1+\alpha }$$\end{document} 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.