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Green's function estimates for lattice Schrödinger operators and applications /

This book presents an overview of recent developments in the area of localization for quasi-periodic lattice Schrödinger operators and the theory of quasi-periodicity in Hamiltonian evolution equations. The physical motivation of these models extends back to the works of Rudolph Peierls and Douglas...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Bourgain, Jean, 1954-2018
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, N.J. : Princeton University Press, ©2005.
©2005
Colección:Annals of mathematics studies ; no. 158.
Temas:
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Frontmatter
  • Contents
  • Acknowledgment
  • Chapter 1. Introduction
  • Chapter 2. Transfer Matrix and Lyapounov Exponent
  • Chapter 3. Herman's Subharmonicity Method
  • Chapter 4. Estimates on Subharmonic Functions
  • Chapter 5. LDT for Shift Model
  • Chapter 6. Avalanche Principle in SL
  • Chapter 7. Consequences for Lyapounov Exponent, IDS, and Green's Function
  • Chapter 8. Refinements
  • Chapter 9. Some Facts about Semialgebraic Sets
  • Chapter 10. Localization
  • Chapter 11. Generalization to Certain Long-Range Models
  • Chapter 12. Lyapounov Exponent and Spectrum
  • Chapter 13. Point Spectrum in Multifrequency Models at Small Disorder
  • Chapter 14. A Matrix-Valued Cartan-Type Theorem
  • Chapter 15. Application to Jacobi Matrices Associated with Skew Shifts
  • Chapter 16. Application to the Kicked Rotor Problem
  • Chapter 17. Quasi-Periodic Localization on the Z
  • Chapter 18. An Approach to Melnikov's Theorem on Persistency of Nonresonant Lower Dimension Tori
  • Chapter 19. Application to the Construction of Quasi-Periodic Solutions of Nonlinear Schrödinger Equations
  • Chapter 20. Construction of Quasi-Periodic Solutions of Nonlinear Wave Equations
  • Appendix.