This paper continues the discussion started in [ 10 ] 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 set are provided in case the phase space is: (A) a uniform neighbourhood 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.

本文继续[10]中有关Arnold关于经典KAM理论及其（现代）发展的遗产的讨论。我们证明了详细而明确的“全局”阿诺德KAM定理，特别是得出了一个非退化的，实解析的，几乎可积分的哈密顿系统到在可封闭的，无处密集的正度量下的可积分系统的惠特尼共轭性。相空间的子集。如果相空间是：（A）任意（有界）集合的均匀邻域乘以\（d \）- torus和（B）具有\（C ^ { 2} \）边界乘以\（d \）- torus。所有常量都明确给出。