This book presents an overview of recent developments in the
area of localization for quasi-periodic lattice Schrodinger
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.""
General
Imprint: |
Princeton University Press
|
Country of origin: |
United States |
Series: |
Annals of Mathematics Studies |
Release date: |
November 2004 |
First published: |
November 2004 |
Authors: |
Jean Bourgain
|
Dimensions: |
235 x 152 x 10mm (L x W x T) |
Format: |
Paperback
|
Pages: |
200 |
Edition: |
New |
ISBN-13: |
978-0-691-12098-0 |
Categories: |
Books
|
LSN: |
0-691-12098-6 |
Barcode: |
9780691120980 |
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