Homoclinic orbits to invariant sets of quasi-integrable exact maps
Homoclinic orbits to invariant sets of quasi-integrable exact maps
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DOI：
10.1017/s0143385700000870
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发表时间：
2000-12
影响因子：
0.9
通讯作者：
P. Bernard
中科院分区：
文献类型：
--
作者：
P. Bernard
可积系统的共振环面被微扰破坏。如果哈密尔顿算子是凸的，它们会产生双曲低维不变环面或奥布里-马瑟不变集。Bolotin证明了双曲环面的同宿轨的存在性，但没有证明Aubry-Mather不变集的同宿轨的存在性。我们解决了这个问题，并获得，对于每个谐振频率，存在一个不变的同宿轨道集。
The resonant tori of an integrable system are destroyed by a perturbation. If the Hamiltonian is convex, they give rise to hyperbolic lower-dimensional invariant tori or to Aubry–Mather invariant sets. Bolotin has proved the existence of homoclinic orbits to the hyperbolic tori but not to the Aubry–Mather invariant sets. We solve this problem and obtain, for each resonant frequency, the existence of an invariant set with homoclinic orbits.