KdV方程和KAM理论 英文PDF电子书下载

Chapter Ⅰ　The Beginning 1

1 Overview 1

Chapter Ⅱ　Classical Background 19

2　Hamiltonian Formalism 19

3　Liouville Integrable Systems 27

4 Birkhoff Integrable Systems 34

5 KAM Theory 39

Chapter Ⅲ　Birkhoff Coordinates 51

6 Background and Results 51

7 Actions 63

8 Angles 69

9 Cartesian Coordinates 74

10 Orthogonality Relations 85

11　The Diffeomorphism Property 91

12　The Symplectomorphism Property 102

Chapter Ⅳ　Perturbed KdV Equations13　The Main Theorems 111

14 Birkhoff Normal Form 118

15 Global Coordinates and Frequencies 127

16 The KAM Theorem 133

17　Proof of the Main Theorems 139

Chapter Ⅴ The KAM Proof 145

18 Set Up and Summary of Main Results 145

19 The Linearized Equation 152

20 The KAM Step 160

21 Iteration and Convergence 165

22 The Excluded Set of Parameters 171

Chapter Ⅵ Kuksin's Lemma 177

23 Kuksin's Lemma 177

Chapter Ⅶ Background Material 187

A Analyticity 187

B Spectra 194

C KdV Hierarchy 207

Chapter Ⅷ Psi-Functions and FrequenciesD Construction of the Psi-Functions 211

E A Trace Formula 223

F Frequencies 227

Chapter Ⅸ Birkhoff Normal FormsG Two Results on Birkhoff Normal Forms 233

H Birkhoff Normal Form of Order 6 240

I Kramer's Lemma 248

J Nondegeneracy of the Second KdV Hamiltonian 252

Chapter Ⅹ Some Technicalities 257

K Symplectic Formalism 257

L Infinite Products 260

M Auxiliary Results 262

References 267

Index 275

Notations 57

1 a-cycles 57

2 Signs of ？ 62

3 Signs of ？ for real q 62

4 Labeling of periodic eigenvalues as q varies 64

5 Isolating neighbourhoods 65

6 A generic △-function 198

7 The set ？a,b？ 202

8 a-and b-cycles for N=2 224

9 a′-and b-cycles with basepoint λ0 for N=2 224

10 Signs of ？ for real q 282