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A refinement of the Hofer-Zehnder theorem on the existence of closed trajectories near a hypersurface

Leonardo Macarini·Felix Schlenk
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Abstract

The Hofer-Zehnder theorem states that almost every hypersurface in a thickening of a hypersurface $S$ in a symplectic manifold $(M,ω)$ carries a closed characteristic provided that $S$ bounds a compact submanifold and $(M,ω)$ has finite capacity. We show that it is enough to assume that the thickening of $S$ has finite capacity.

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Leonardo Macarini, Felix Schlenk. 2003-05-09. A refinement of the Hofer-Zehnder theorem on the existence of closed trajectories near a hypersurface. https://arxiv.org/abs/math/0305148

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