Remarks about the \(C^{\infty }\)-closing lemma for 3-dimensional Reeb flows
type: Item
instance of: scholarly article
title: Remarks about the \(C^{\infty }\)-closing lemma for 3-dimensional Reeb flows
zbMATH Open document ID: 1485.53098
DOI: 10.1215/21562261-2021-0003
author: Kei Irie
published in: Kyoto Journal of Mathematics
publication date: 2021-07-07T00:00:00Z
review text: 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.
reviewed by: Antonella Nannicini
Mathematics Subject Classification ID: 53D10
Mathematics Subject Classification ID: 53D42
zbMATH DE Number: 7369028
zbMATH Keywords: closing lemma
zbMATH Keywords: embedded contact homology
zbMATH Keywords: periodic Reeb orbits
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/21562261-2021-0003
OpenAlex ID: W3156845768
Wikidata QID: Q125064111
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description: scientific article; zbMATH DE number 7369028