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arXiv · 1309.4982

Trapped Reeb orbits do not imply periodic ones

Hansjörg Geiges·Nena Röttgen·Kai Zehmisch
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Abstract

We construct a contact form on R^{2n+1}, n at least 2, equal to the standard contact form outside a compact set and defining the standard contact structure on all of R^{2n+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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Hansjörg Geiges, Nena Röttgen, Kai Zehmisch. 2013-09-19. Trapped Reeb orbits do not imply periodic ones. https://doi.org/10.1007/s00222-014-0500-9

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