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A REFINEMENT OF THE HOFER–ZEHNDER THEOREM ON THE EXISTENCE OF CLOSED CHARACTERISTICS NEAR A HYPERSURFACE

Published online by Cambridge University Press:  10 March 2005

LEONARDO MACARINI
Affiliation:
Instituto de Matemática Pura, e Aplicada – IMPA, Estrada Dona Castorina, 110 – Jardim Botânico, 22460-320 Rio de Janeiro RJ, [email protected]
FELIX SCHLENK
Affiliation:
Mathematisches Institut, Universität Leipzig, 04109 Leipzig, [email protected]
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Abstract

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.

Type
Papers
Copyright
© The London Mathematical Society 2005

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