准周期哈密顿运动、标度不变性、谐振子
动力系统
2020-07-21 v5
摘要
Kolmogorov、Arnold与Moser的工作恰好出现在Wilson提出统计力学的重整化群方法之前：它可被归类为一种多尺度方法，这种方法也出现在关于傅里叶级数收敛性、欧几里得量子场构造、或 Navier-Stokes 流体小尺度行为的标度分析等工作中，仅举数例，这些工作引发了大量进一步的问题。在本综述中，KAM定理的证明将作为一个经典重整化问题呈现，以谐振子作为一个“平凡”不动点。
引用
@article{arxiv.1810.07786,
title = {Quasi periodic Hamiltonian Motions, Scale Invariance, Harmonic Oscillators},
author = {Giovanni Gallavotti},
journal= {arXiv preprint arXiv:1810.07786},
year = {2020}
}
备注
FM05-18: v1-v.2-v.3 contained a mistake, now corrected (and simplified) here. In the new (version 5): symbol J_1 introduced in Eq.2.4, which is rewritten in a form suitable for the derivation of Eq.(5.4),(5.5). The latter although correct were not properly derived. Eq. 5.7 includes the bound on J_1 and the labels in the formulae of Sec.5 are updated