Remarks about the \(C^{\infty }\)-closing lemma for 3-dimensional Reeb flows (Q2038537)

By using embedded contact homology, in a previous paper [J. Mod. Dyn. 9, 357--363 (2015; Zbl 1353.37125)], the author proves a \(C^\infty\)-closing lemma and a \(C^\infty\)-generic density theorem for 3-dimensional Reeb flows. One of the main results of this paper is a refinement of \(C^\infty\)-closing lemma, precisely he proves that given a \(C^\infty\)-generic contact form on a closed 3-manifold the union of periodic Reeb orbits representing Embedded Contact Homology is dense. The other result is a real analytic version of the \(C^\infty\)-closing lemma of the previous paper. In the paper, after recalling quantitative aspects of embedded contact homology, the author discusses asymptotic behaviour of periodic Reeb orbits representing embedded contact homology classes. Then the main results are proved and related questions and conjectures are discussed.