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arXiv · 1210.5037

Closed Reeb orbits on the sphere and symplectically degenerate maxima

Viktor L. Ginzburg·Doris Hein·Umberto L. Hryniewicz·Leonardo Macarini
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Abstract

We show that the existence of one simple closed Reeb orbit of a particular type (a symplectically degenerate maximum) forces the Reeb flow to have infinitely many periodic orbits. We use this result to give a different proof of a recent theorem of Cristofaro-Gardiner and Hutchings asserting that every Reeb flow on the standard contact three-sphere has at least two periodic orbits. Our methods are based on adapting the machinery originally developed for proving the Hamiltonian Conley conjecture to the contact setting.

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Viktor L. Ginzburg, Doris Hein, Umberto L. Hryniewicz, Leonardo Macarini. 2012-10-18. Closed Reeb orbits on the sphere and symplectically degenerate maxima. https://arxiv.org/abs/1210.5037

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