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

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

2003-05-09

arxiv.org/abs/math/0305148v1

Mathematics

Symplectic Geometry

4 pages, 1 figure

Scientific paper

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.

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