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A Refinement of the Hofer–Zehnder Theorem on the Existence of Closed Characteristics Near a Hypersurface
Author(s) -
Macarini Leonardo,
Schlenk Felix
Publication year - 2005
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609304003923
Subject(s) - mathematics , hypersurface , pure mathematics , mathematical analysis
The Hofer–Zehnder theorem states that almost every hypersurface in a thickening of a hypersurface S in a symplectic manifold ( M , ω) carries a closed characteristic, provided that S bounds a compact submanifold and ( M , ω) 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).