A Refinement of the Hofer–Zehnder Theorem on the Existence of Closed Characteristics Near a Hypersurface

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. It is shown that it is enough to assume that the thickening of S has finite capacity. 2000 Mathematics Subject Classification 70H12 (primary), 34C25 (secondary).