Preprint A240/2003
A refinement of the Hofer-Zehnder theorem on the existence of closed trajectories near a hypersurface

Felix Schlenk | Macarini, Leonardo

**Keywords: **

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