Symplectic topology of Mañé's critical values
Symplectic topology of Mañé's critical values
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Mañé 临界值的辛拓扑
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
G. Paternain
中科院分区：
文献类型：
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作者：
K. Cieliebak;U. Frauenfelder;G. Paternain
研究了扭余切丛上力学哈密顿量的能量超曲面的动力学和辛拓扑。我们特别注意周期轨道，可扩展性，稳定性和接触型属性，以及发生在马内临界值c的变化。我们的主要工具是Rabinowitz Floer同源性。我们表明，它是定义为超曲面，无论是稳定驯服或虚拟接触，它是不变的同伦在这些类。如果位形空间允许一个负曲率的度量，那么Rabinowitz Floer同调对于能级k > c不会为零，因此，这些能级集是不可置换的。我们提供了一大类例子，其中Rabinowitz Floer同调对于能级k > c是非零的，但对于k < c为零，因此高于和低于c的能级不能由稳定的驯服同伦连接。此外，我们还证明了对于严格的1=4-箍缩负曲率和非精确磁场，所有足够高的能级都是不稳定的，只要基流形的维数是偶数并且不等于2。53D40; 37D40
We study the dynamics and symplectic topology of energy hypersurfaces of mechanical Hamiltonians on twisted cotangent bundles. We pay particular attention to periodic orbits, displaceability, stability and the contact type property, and the changes that occur at the Mane critical value c . Our main tool is Rabinowitz Floer homology. We show that it is defined for hypersurfaces that are either stable tame or virtually contact, and that it is invariant under homotopies in these classes. If the configuration space admits a metric of negative curvature, then Rabinowitz Floer homology does not vanish for energy levels k > c and, as a consequence, these level sets are not displaceable. We provide a large class of examples in which Rabinowitz Floer homology is nonzero for energy levels k > c but vanishes for k < c , so levels above and below c cannot be connected by a stable tame homotopy. Moreover, we show that for strictly 1=4‐pinched negative curvature and nonexact magnetic fields all sufficiently high energy levels are nonstable, provided that the dimension of the base manifold is even and different from two. 53D40; 37D40
稳定哈密顿拓扑的第一步
DOI：
10.4171/jems/505
发表时间：
2015
期刊：
arXiv: Symplectic Geometry
影响因子：
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作者：
K. Cieliebak;E. Volkov
通讯作者：
E. Volkov