Trapped Reeb orbits do not imply periodic ones

We construct a contact form on R 2 n + 1 , n ≥ 2 , equal to the standard contact form outside a compact set and defining the standard contact structure on all of R 2 n + 1 , which has trapped Reeb orbits, including a torus invariant under the Reeb flow, but no closed Reeb orbits. This answers a ques...

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Bibliographic Details
Published inInventiones mathematicae Vol. 198; no. 1; pp. 211 - 217
Main Authors Geiges, Hansjörg, Röttgen, Nena, Zehmisch, Kai
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2014
Springer Nature B.V
Subjects
Construction standards
Contact
Invariants
Mathematics
Mathematics and Statistics
Orbits
Texts
37C70
37C27
53D10
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Summary:We construct a contact form on R 2 n + 1 , n ≥ 2 , equal to the standard contact form outside a compact set and defining the standard contact structure on all of R 2 n + 1 , which has trapped Reeb orbits, including a torus invariant under the Reeb flow, but no closed Reeb orbits. This answers a question posed by Helmut Hofer.
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ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-014-0500-9