Trapped Reeb orbits do not imply periodic ones

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• 作者：Hansj?rg Geiges ; Nena R?ttgen ; Kai Zehmisch
• 关键词：37C27 ; 37C70 ; 53D10
• 刊名：Inventiones Mathematicae
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：198
• 期：1
• 页码：211-217
• 全文大小：117 KB
• 参考文献：1. Bangert, V., R?ttgen, N.: Isoperimetric inequalities for minimal submanifolds in Riemannian manifolds: a counterexample in higher codimension. Calc. Var. Partial Differ. Equ. 45, 455-66 (2012) CrossRef
  2. Bramham, B., Hofer, H.: First steps towards a symplectic dynamics. Surv. Differ. Geom. 17, 127-78 (2012) CrossRef
  3. Eliashberg, Ya., Hofer, H.: A Hamiltonian characterization of the three-ball. Differ. Integr. Equ. 7, 1303-324 (1994)
  4. Geiges, H.: An Introduction to Contact Topology, Cambridge Stud. Adv. Math., vol 109. Cambridge University Press, Cambridge (2008) CrossRef
  5. R?ttgen, N.: A contact cylinder with standard boundary and a bounded Reeb orbit but no periodic Reeb orbit. (2013) (preprint)
  
• 作者单位：Hansj?rg Geiges (1)
  Nena R?ttgen (2)
  Kai Zehmisch (1)
  
  1. Mathematisches Institut, Universit?t zu K?ln, Weyertal 86-0, 50931?, K?ln, Germany
  2. Mathematisches Institut, Albert-Ludwigs-Universit?t Freiburg, Eckerstr.?1, 79104?, Freiburg, Germany
  
• ISSN：1432-1297

文摘

We construct a contact form on \(\mathbb {R}^{2n+1}\) , \(n\ge 2\) , equal to the standard contact form outside a compact set and defining the standard contact structure on all of \(\mathbb {R}^{2n+1}\) , 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.