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34c25 (secondary)

Bulletin of the London Mathematical Society (1)

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A REFINEMENT OF THE HOFER–ZEHNDER THEOREM ON THE EXISTENCE OF CLOSED CHARACTERISTICS NEAR A HYPERSURFACE
LEONARDO MACARINI, FELIX SCHLENK
Journal:

Bulletin of the London Mathematical Society / Volume 37 / Issue 2 / March 2005

Published online by Cambridge University Press:

10 March 2005, pp. 297-300

Print publication:

March 2005
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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. It is shown that it is enough to assume that the thickening of $S$ has finite capacity.