Exact Lagrangian submanifolds, Lagrangian spectral invariants and Aubry–Mather theory
Exact Lagrangian submanifolds, Lagrangian spectral invariants and Aubry–Mather theory
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精确拉格朗日子流形、拉格朗日谱不变量和奥布里-马瑟理论
DOI：
10.1017/s0305004117000561
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发表时间：
2016
影响因子：
0.8
通讯作者：
Joana OLIVEIRA DOS SANTOS
中科院分区：
文献类型：
--
作者：
Lino Amorim;Y. Oh;Joana OLIVEIRA DOS SANTOS
在可定向闭流形的余切束上构造紧致精确拉格朗日的图选择器。这种构造结合了Oh提出的拉格朗日谱不变量和Abouzaid关于余切束的Fukaya范畴的结果。我们还引入了Lipschitz-exact lagrangian的概念，并证明了它们允许图选择器的适当推广。然后，我们继Bernard-Oliveira dos Santos之后，利用这些结果给出了Tonelli hamilton的Aubry集和Mañé集的新特征，并推广了Arnaud关于lagrange不变量在这种hamilton流下的结果。
Abstract We construct graph selectors for compact exact Lagrangians in the cotangent bundle of an orientable, closed manifold. The construction combines Lagrangian spectral invariants, developed by Oh, and results, by Abouzaid, about the Fukaya category of a cotangent bundle. We also introduce the notion of Lipschitz-exact Lagrangians and prove that these admit an appropriate generalisation of graph selector. We then, following Bernard–Oliveira dos Santos, use these results to give a new characterisation of the Aubry and Mañé sets of a Tonelli Hamiltonian and to generalise a result of Arnaud on Lagrangians invariant under the flow of such Hamiltonians.
影响因子：
2.5
作者：
Y. Oh
通讯作者：
Y. Oh