Minimal invariant tori in the resonant regions for nearly integrable Hamiltonian systems
Minimal invariant tori in the resonant regions for nearly integrable Hamiltonian systems
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DOI：
10.1090/s0002-9947-05-03674-3
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发表时间：
2005-03
影响因子：
1.3
通讯作者：
Chong-Quing Cheng
中科院分区：
文献类型：
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作者：
Chong-Quing Cheng
考虑一个真实的KAM型解析哈密顿系统H(p,q) = N(p) + p (p,q)，它有N个自由度（N | 2）并且在p中是正定的。设Ω = {Ω∈R N | = 0, k∈Z N}。本文证明了对于Ω中的大多数旋转向量，在（n - 1）维勒贝格测度意义上，至少存在一个（n - 1）维不变环面。这些环面是相应最小测度的支撑。该集合上的勒贝格测度估计对任何扰动都一致有效。
Consider a real analytical Hamiltonian system of KAM type H(p,q) = N(p) + P(p,q) that has n degrees of freedom (n > 2) and is positive definite in p. Let Ω = {ω∈R n | = 0, k∈Z n }. In this paper we show that for most rotation vectors in Ω, in the sense of (n - 1)-dimensional Lebesgue measure, there is at least one (n - 1)-dimensional invariant torus. These tori are the support of corresponding minimal measures. The Lebesgue measure estimate on this set is uniformly valid for any perturbation.