Trapped Reeb orbits do not imply periodic ones
A theorem by \textit{Y. Eliashberg} and \textit{H. Hofer} [Differ. Integral Equ. 7, No. 5--6, 1303--1324 (1994; Zbl 0803.58045)] states that any contact form \(\alpha\) on \(\mathbb R^3\) which equals the standard form outside a compact set and whose Reeb vector field does not have any periodic orbits, is diffeomorphic to the standard one. In terms of the Reeb vector field, this is equivalent to say that if the Reeb vector field of \(\alpha\) has a trapped orbit, then it also has a periodic orbit. H. Hofer conjectured the higher-dimensional analogue of this result, but in this paper the authors disprove that conjecture by an example.
scientific article; zbMATH DE number 6362528
scientific article