论文标题
V.I.阿诺德的“全局” kaM定理和几何措施估计值
V.I. Arnold's "Global" KAM Theorem and geometric measure estimates
论文作者
论文摘要
本文继续讨论始于[CK19]，涉及阿诺德在古典KAM理论和（其中一些）现代发展的遗产。我们证明了一种详细而明确的“全球” Arnold的KAM定理，尤其是在封闭的，无处不在的，无处可靠的积极测量的相位空间子集上，非分级，实地，无效的Hamiltony系统的惠特尼共轭与可集成的系统的共同系统。在相位空间中，提供了Kolmogorov的详细度量估计值：（a）任意（边界）设置的均匀邻域d-torus和（b）具有$ c^2 $ bouncy the d torus d-torus的域。所有常数都明确给出。
This paper continues the discussion started in [CK19] concerning Arnold's legacy on classical KAM theory and (some of) its modern developments. We prove a detailed and explicit `global' Arnold's KAM Theorem, which yields, in particular, the Whitney conjugacy of a non-degenerate, real-analytic, nearly-integrable Hamiltonian system to an integrable system on a closed, nowhere dense, positive measure subset of the phase space. Detailed measure estimates on the Kolmogorov's set are provided in the case the phase space is: (A) a uniform neighborhood of an arbitrary (bounded) set times the d-torus and (B) a domain with $C^2$ boundary times the d-torus. All constants are explicitly given.
