TABLE OF CONTENTS: Acknowledgment v
CHAPTER 1: Introduction 1
CHAPTER 2: Transfer Matrix and Lyapounov Exponent 11
CHAPTER 3: Herman's Subharmonicity Method 15
CHAPTER 4: Estimates on Subharmonic Functions 19
CHAPTER 5: LDT for Shift Model 25
CHAPTER 6: Avalanche Principle in SL2( R ) 29
CHAPTER 7: Consequences for Lyapounov Exponent, IDS, and Green's Function 31
CHAPTER 8: Refinements 39
CHAPTER 9: Some Facts about Semialgebraic Sets 49
CHAPTER 10: Localization 55
CHAPTER 11: Generalization to Certain Long-Range Models 65
CHAPTER 12: Lyapounov Exponent and Spectrum 75
CHAPTER 13: Point Spectrum in Multifrequency Models at Small Disorder 87
CHAPTER 14: A Matrix-Valued Cartan-Type Theorem 97
CHAPTER 15: Application to Jacobi Matrices Associated with Skew Shifts 105
CHAPTER 16: Application to the Kicked Rotor Problem 117
CHAPTER 17: Quasi-Periodic Localization on the Z d -lattice ( d > 1) 123
CHAPTER 18: An Approach to Melnikov's Theorem on Persistency of Non-resonant Lower Dimension Tori 133
CHAPTER 19: Application to the Construction of Quasi-Periodic Solutions of Nonlinear Schrödinger Equations 143
CHAPTER 20: Construction of Quasi-Periodic Solutions of Nonlinear Wave Equations 159
Appendix 169
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