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Bulletin of the London Mathematical Society 2005 37(2):297-300; doi:10.1112/S0024609304003923
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© London Mathematical Society

A Refinement of the Hofer–Zehnder Theorem on the Existence of Closed Characteristics Near a Hypersurface

Leonardo Macarini and Felix Schlenk

Instituto de Matemática Pura, e Aplicada – IMPA Estrada Dona Castorina, 110 – Jardim Botânico, 22460-320 Rio de Janeiro RJ, Brazil leonardo{at}impa.br
Mathematisches Institut, Universität Leipzig 04109 Leipzig, Germany schlenk{at}math.uni-leipzig.de

Received 23 May 2003. Revision received 11 February 2004.

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. 2000 Mathematics Subject Classification 70H12 (primary), 34C25 (secondary).

First author partially supported by CNPq-PROFIX, Brazil.


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