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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67422The 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.4 pages, 1 figureSymplectic GeometryDynamical SystemsA refinement of the Hofer-Zehnder theorem on the existence of closed trajectories near a hypersurfacetext