Annalen Closed characteristics on non-compact hypersurfaces in R 2 n
Annalen Closed characteristics on non-compact hypersurfaces in R 2 n
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Annalen R 2 n 中非紧超曲面的闭合特性
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
R. Vandervorst
中科院分区：
文献类型：
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作者：
J. B. Berg;F. Pasquotto;R. Vandervorst
维泰博证明了任何（2n − 1）维紧致超曲面M（R2 n，ω）至少有一个闭特征。这一结果证明了标准辛空间（R2 n，ω）上的Weinstein猜想。这个定理的各种扩展已经得到，因为所有的紧超曲面。本文考虑由力学Hamilton算子生成的非紧超曲面M ∈（R2 n，ω），并证明了维泰博的一个类似结果.主要结果提供了上半同调群Hi（M），i = n，. . .，2n-1，以及在非紧情形（包括紧情形）下闭特征的存在性。
Viterbo demonstrated that any (2n − 1)-dimensional compact hypersurface M ⊂ (R2n, ω) of contact type has at least one closed characteristic. This result proved the Weinstein conjecture for the standard symplectic space (R2n, ω). Various extensions of this theorem have been obtained since, all for compact hypersurfaces. In this paper we consider non-compact hypersurfaces M ⊂ (R2n, ω) coming from mechanical Hamiltonians, and prove an analogue of Viterbo’s result. The main result provides a strong connection between the top half homology groups Hi (M), i = n, . . . , 2n − 1, and the existence of closed characteristics in the non-compact case (including the compact case).