书籍介绍
《KdV方程和KAM理论(影印版)》介绍了可积偏微分方程理论的两个方面。第一个方面是可积偏微分方程的正规形式理论，以很重要的非线性可积偏微分方程——周期的Korteweg de Vries方程为例来阐述这个正规形式理论，这构成了书的“KdV”部分。第二个方面是可积偏微分方程的哈密顿摄动理论，它的原始模型是由Kolmogorovk，Arnold和Moser发展起来的针对有限维系统的理论，这构成了书的“KAM'’部分。
《KdV方程和KAM理论(影印版)》不仅是为可积偏微分方程理论和哈密顿摄动理论的专家所写，也为远离这些领域的研究工作者和研究生所写。为了使《KdV方程和KAM理论(影印版)》达到自密的程度，作者增加了描述有限维哈密顿系统的一章，所省略的证明都可以在熟知的教科书中找到。
目录
Chapter Ⅰ The Beginning 1 OverviewChapter Ⅱ Classical Background 2 Hamiltonian Formalism 3 Liouviile Integrable Systems 4 Birkhoff Integrable Systems 5 KAMTheoryChapter Ⅲ Birkhoff Coordinates 6 Background and Results 7 Actions 8 Angles 9 Cartesian Coordinates 10 Orthogonality Relations 11 The Diffeomorphism Property 12 The Symplectomorphism PropertyChapter Ⅳ Perturbed KdV Equations 13 The Main Theorems 14 Birkhoff Normal Form 15 Global Coordinates and Frequencies 16 The KAM Theorem 17 Proof of the Main TheoremsChapter Ⅴ The KAM Proof 18 Set Up and Summary of Main Results 19 The Linearized Equation 20 TheKAMStep 21 Iteration and Convergence 22 The Excluded Set of ParametersChapter Ⅵ Kuksin's Lemma 23 Kuksin's LemmaChapter Ⅶ Background Material A Analyticity B Spectra C KdV HierarchyChapter Ⅷ Psi-Functions and Frequencies D Construction of the Psi-Functions E A Trace Formula F FrequenciesChapter Ⅸ Birkhoff Normal Forms G Two Results on Birkhoff Normal Forms H Birkhoff Normal Form of Order 6 I Kramer's Lemma J Nondegeneracy of the Second KdV HamiltonianChapter Ⅹ Some Technicalities K Symplectic Formalism L Infinite Products M Auxiliary ResultsReferencesIndexNotations
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