余切丛中哈密顿系统的周期轨道
Periodic orbits for Hamiltonian systems in cotangent bundles
摘要：
本文证明了任意紧流形$M$的余切丛上某些含时哈密顿系统至少存在$cl(M)$周期轨道.这些哈密尔顿算子不一定是凸的，但它们满足$M$上的黎曼度量给出的某个边界条件。我们通过将时间1映射分解为"辛扭曲映射“的乘积来离散变分问题。第二个定理讨论负曲率流形中的同伦非平凡轨道。
英文摘要：
We prove the existence of at least $cl(M)$ periodic orbits for certain time dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold $M$. These Hamiltonians are not necessarily convex but they satisfy a certain boundary condition given by a Riemannian metric on $M$. We discretize the variational problem by decomposing the time 1 map into a product of ``symplectic twist maps''. A second theorem deals with homotopically non trivial orbits in manifolds of negative curvature.
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