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

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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