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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  and
FELIX SCHLENK
LEONARDO MACARINI
Affiliation:
Instituto de Matemática Pura, e Aplicada – IMPA, Estrada Dona Castorina, 110 – Jardim Botânico, 22460-320 Rio de Janeiro RJ, Brazilleonardo@impa.br
FELIX SCHLENK
Affiliation:
Mathematisches Institut, Universität Leipzig, 04109 Leipzig, Germanyschlenk@math.uni-leipzig.de
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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.

Keywords

70H12 (primary)34C25 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 2 , March 2005 , pp. 297 - 300
Copyright
© The London Mathematical Society 2005

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