Green's Function Estimates for Lattice Schrödinger Operators and Applications. (AM-158) / / Jean Bourgain.
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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Year of Publication: | 2004 |
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Bourgain, Jean, author. aut http://id.loc.gov/vocabulary/relators/aut Green's Function Estimates for Lattice Schrödinger Operators and Applications. (AM-158) / Jean Bourgain. Princeton, NJ : Princeton University Press, [2004] ©2005 1 online resource (200 p.) : 14 line illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 158 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 SL2(R) -- 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 Zd-lattice (d > 1) -- 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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 R. Hofstadter, and the models themselves have been a focus of mathematical research for two decades. Jean Bourgain here sets forth the results and techniques that have been discovered in the last few years. He puts special emphasis on so-called "non-perturbative" methods and the important role of subharmonic function theory and semi-algebraic set methods. He describes various applications to the theory of differential equations and dynamical systems, in particular to the quantum kicked rotor and KAM theory for nonlinear Hamiltonian evolution equations. Intended primarily for graduate students and researchers in the general area of dynamical systems and mathematical physics, the book provides a coherent account of a large body of work that is presently scattered in the literature. It does so in a refreshingly contained manner that seeks to convey the present technological "state of the art." Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Evolution equations. Green's functions. Hamiltonian systems. Schr̈odinger operators. MATHEMATICS / Differential Equations / General. bisacsh Almost Mathieu operator. Analytic function. Anderson localization. Betti number. Cartan's theorem. Chaos theory. Density of states. Dimension (vector space). Diophantine equation. Dynamical system. Equation. Existential quantification. Fundamental matrix (linear differential equation). Green's function. Hamiltonian system. Hermitian adjoint. Infimum and supremum. Iterative method. Jacobi operator. Linear equation. Linear map. Linearization. Monodromy matrix. Non-perturbative. Nonlinear system. Normal mode. Parameter space. Parameter. Parametrization. Partial differential equation. Periodic boundary conditions. Phase space. Phase transition. Polynomial. Renormalization. Self-adjoint. Semialgebraic set. Special case. Statistical significance. Subharmonic function. Summation. Theorem. Theory. Transfer matrix. Transversality (mathematics). Trigonometric functions. Trigonometric polynomial. Uniformization theorem. Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502 print 9780691120980 https://doi.org/10.1515/9781400837144 https://www.degruyter.com/isbn/9781400837144 Cover https://www.degruyter.com/document/cover/isbn/9781400837144/original |
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English |
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author |
Bourgain, Jean, Bourgain, Jean, |
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Bourgain, Jean, Bourgain, Jean, Green's Function Estimates for Lattice Schrödinger Operators and Applications. (AM-158) / Annals of Mathematics Studies ; 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 SL2(R) -- 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 Zd-lattice (d > 1) -- 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 |
author_facet |
Bourgain, Jean, Bourgain, Jean, |
author_variant |
j b jb j b jb |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Bourgain, Jean, |
title |
Green's Function Estimates for Lattice Schrödinger Operators and Applications. (AM-158) / |
title_full |
Green's Function Estimates for Lattice Schrödinger Operators and Applications. (AM-158) / Jean Bourgain. |
title_fullStr |
Green's Function Estimates for Lattice Schrödinger Operators and Applications. (AM-158) / Jean Bourgain. |
title_full_unstemmed |
Green's Function Estimates for Lattice Schrödinger Operators and Applications. (AM-158) / Jean Bourgain. |
title_auth |
Green's Function Estimates for Lattice Schrödinger Operators and Applications. (AM-158) / |
title_alt |
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 SL2(R) -- 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 Zd-lattice (d > 1) -- 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 |
title_new |
Green's Function Estimates for Lattice Schrödinger Operators and Applications. (AM-158) / |
title_sort |
green's function estimates for lattice schrödinger operators and applications. (am-158) / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2004 |
physical |
1 online resource (200 p.) : 14 line illus. Issued also in print. |
contents |
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 SL2(R) -- 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 Zd-lattice (d > 1) -- 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 |
isbn |
9781400837144 9783110494914 9783110442502 9780691120980 |
callnumber-first |
Q - Science |
callnumber-subject |
QC - Physics |
callnumber-label |
QC174 |
callnumber-sort |
QC 3174.17 S3 |
url |
https://doi.org/10.1515/9781400837144 https://www.degruyter.com/isbn/9781400837144 https://www.degruyter.com/document/cover/isbn/9781400837144/original |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515.39 |
dewey-sort |
3515.3 19 |
dewey-raw |
515.3 9 |
dewey-search |
515.3 9 |
doi_str_mv |
10.1515/9781400837144 |
oclc_num |
1004872417 |
work_keys_str_mv |
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status_str |
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ids_txt_mv |
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cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
is_hierarchy_title |
Green's Function Estimates for Lattice Schrödinger Operators and Applications. (AM-158) / |
container_title |
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