Energy capacity inequalities via an action selector
Energy capacity inequalities via an action selector
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通过行动选择器的能量容量不平等
DOI：
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发表时间：
2004
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：
U. Frauenfelder;V. Ginzburg;F. Schlenk
动作选择器以适当的方式将该哈密顿量的动作值与辛流形上的每个紧支撑的哈密顿量相关联。
众所周知，作用量选择子存在于一大类辛流形上。我们展示了作用量选择子的存在如何导致Gromov宽度、Hofer-Zehnder容量和位移能量之间的尖锐的能量容量不等。我们还得到了接触型超曲面上闭特征的最小作用的精确下界。
An action selector associates, in a suitable way, to each compactly supported Hamiltonian on a symplectic manifold an action value of the Hamiltonian.
Action selectors are known to exist for a broad class of symplectic manifolds. We show how the existence of an action selector leads to sharp energy capacity inequalities between the Gromov width, the Hofer--Zehnder capacity, and the displacement energy. We also obtain sharp lower bounds for the smallest action of a closed characteristic on contact type hypersurfaces.