A Refinement of the Hofer–Zehnder Theorem on the Existence of Closed Characteristics Near a Hypersurface
A Refinement of the Hofer–Zehnder Theorem on the Existence of Closed Characteristics Near a Hypersurface
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超曲面附近存在闭特征的 Hofer-Zehnder 定理的改进
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
F. Schlenk
中科院分区：
文献类型：
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作者：
Leonardo Macarini;F. Schlenk
Hofer-Zehnder 定理指出，辛流形 (M, ω) 中超曲面 S 的加厚中的几乎每个超曲面都具有闭合特征，前提是 S 限制紧致子流形且 (M, ω) 具有有限容量。结果表明，假设 S 的增厚具有有限容量就足够了。 2000 年数学科目分类 70H12（小学）、34C25（中学）。
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).