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：2010-07
出版社：高等教育出版社
- 高等教育出版社
- 9787040286984
- 1版
- 37747
- 44258475-1
- 平装
- 异16开
- 2010-07
- 450
- 279
- 理学
- 数学
- 数学类
- 研究生及以上
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
