KdV方程和KAM理论（影印版） / 天元基金影印数学丛书
￥22.90定价
作者： Kappeler and Poschel
出版时间：2010年7月
出版社：高等教育出版社
- 高等教育出版社
- 9787040286984
- 1版
- 37747
- 0045150271-0
- 异16开
- 2010年7月
- 450
- 279
- 理学
- 数学
- O241.82
- 数学类
- 研究生
内容简介
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 Overview 1
Chapter II Classical Background
2 Hamiltonian Formalism
3 Liouville Integrable Systems
4 Birkhoff Integrable Systems
5 KAM Theory
Chapter III Birkhoff Coordinates
6 Background and Results
7 Actions
8 Angles
9 Cartesian Coordinates
10 Orthogonality Relations
11 The Diffeomorphism Property
12 The Symplectomorphism Property
Chapter 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 Theorems
Chapter V The KAM Proof
18 Set Up and Summary of Main Results
19 The Linearized Equation
20 The KAM Step
2 1 Iteration and Convergence
22 The Excluded Set 0f Parameters
Chapter VI Kuksins Lemma
23 KuksinS Lemma
Chapter VII Background Material
A Analyticity
B Spectra
C KdV Hierarchy
Chapter VIII Psi-Functions and Frequencies
D Construction of the Psi-Functions
E ATraceFormula
F Frequencies
Chapter IX Birkhoff Normal Forms
G TwO Resuits on Birkhoff Normal Forms
H BirkhoffNormal Form oforder
I KramerS Lemma
J Nondegeneracy of the Second KdV Hamiltonian
Chapter X Some Technicalities
K Symplectic Formalism
L InfiniteProducts
M Auxiliary Results
Referenees
Index
Notations
1 Overview 1
Chapter II Classical Background
2 Hamiltonian Formalism
3 Liouville Integrable Systems
4 Birkhoff Integrable Systems
5 KAM Theory
Chapter III Birkhoff Coordinates
6 Background and Results
7 Actions
8 Angles
9 Cartesian Coordinates
10 Orthogonality Relations
11 The Diffeomorphism Property
12 The Symplectomorphism Property
Chapter 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 Theorems
Chapter V The KAM Proof
18 Set Up and Summary of Main Results
19 The Linearized Equation
20 The KAM Step
2 1 Iteration and Convergence
22 The Excluded Set 0f Parameters
Chapter VI Kuksins Lemma
23 KuksinS Lemma
Chapter VII Background Material
A Analyticity
B Spectra
C KdV Hierarchy
Chapter VIII Psi-Functions and Frequencies
D Construction of the Psi-Functions
E ATraceFormula
F Frequencies
Chapter IX Birkhoff Normal Forms
G TwO Resuits on Birkhoff Normal Forms
H BirkhoffNormal Form oforder
I KramerS Lemma
J Nondegeneracy of the Second KdV Hamiltonian
Chapter X Some Technicalities
K Symplectic Formalism
L InfiniteProducts
M Auxiliary Results
Referenees
Index
Notations
