Singular Hamiltonian systems and symplectic capacities
Singular Hamiltonian systems and symplectic capacities
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奇异哈密顿系统和辛容量
DOI：
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发表时间：
1996
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通讯作者：
A. Künzle
中科院分区：
文献类型：
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作者：
A. Künzle
本文的目的是发展的基础理论的哈密顿系统与不可微的汉密尔顿功能，已成为重要的辛拓扑。引入了一个特征微分包含，并对某些凸Hamilton算子建立了它与Hamilton包含的等价性。我们给出了两个反例，表明光滑系统的基本性质被违反的非光滑拟凸淹没，例如，即使是能量守恒，但凸淹没。这也意味着，凸性假设决定，虽然不是辛不变的，辛几何的极限情况。本文综述了这一理论的一些应用：一般凸集的辛容度，辛积和辛容度的一个乘积公式。
The purpose of this paper is to develop the basics of a theory of Hamiltonian systems with non-differentiable Hamilton functions which have become important in symplectic topology. A characteristic differential inclusion is introduced and its equivalence to Hamiltonian inclusions for certain convex Hamiltonians is established. We give two counterexamples showing that basic properties of smooth systems are violated for non-smooth quasiconvex submersions, e.g. even the energy conservation which nevertheless holds for convex submersions. This also implies that the convexity assumption determines, although not symplectically invariant, a limit case for symplectic geometry. Some applications of this theory are reviewed: symplectic capacities for general convex sets, the symplectic product and a product formula for symplectic capacities.