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100   $a20140904h20052005  uy             0
101 0 $aeng
135   $aurnn#---|u||u
181   $ctxt
182   $cc
183   $acr
200 10$aGreen's function estimates for lattice Schro?dinger operators and applications /$fJ. Bourgain
210  1$aPrinceton, New Jersey :$cPrinceton University Press,$d2005.
210  4$d©2005
215   $a1 online resource (184 p.)
225 1 $aAnnals of Mathematics Studies ;$vNumber 158
300   $aDescription based upon print version of record.
311 0 $a1-322-07571-9 
311 0 $a0-691-12097-8 
320   $aIncludes bibliographical references at the end of each chapters.
327   $tFront matter --$tContents --$tAcknowledgment --$tChapter 1. Introduction --$tChapter 2. Transfer Matrix and Lyapounov Exponent --$tChapter 3. Herman's Subharmonicity Method --$tChapter 4. Estimates on Subharmonic Functions --$tChapter 5. LDT for Shift Model --$tChapter 6. Avalanche Principle in SL2(R) --$tChapter 7. Consequences for Lyapounov Exponent, IDS, and Green's Function --$tChapter 8. Refinements --$tChapter 9. Some Facts about Semialgebraic Sets --$tChapter 10. Localization --$tChapter 11. Generalization to Certain Long-Range Models --$tChapter 12. Lyapounov Exponent and Spectrum --$tChapter 13. Point Spectrum in Multifrequency Models at Small Disorder --$tChapter 14. A Matrix-Valued Cartan-Type Theorem --$tChapter 15. Application to Jacobi Matrices Associated with Skew Shifts --$tChapter 16. Application to the Kicked Rotor Problem --$tChapter 17. Quasi-Periodic Localization on the Zd-lattice (d > 1) --$tChapter 18. An Approach to Melnikov's Theorem on Persistency of Nonresonant Lower Dimension Tori --$tChapter 19. Application to the Construction of Quasi-Periodic Solutions of Nonlinear Schrödinger Equations --$tChapter 20. Construction of Quasi-Periodic Solutions of Nonlinear Wave Equations --$tAppendix
330   $aThis book presents an overview of recent developments in the area of localization for quasi-periodic lattice Schrödinger operators and the theory of quasi-periodicity in Hamiltonian evolution equations. The physical motivation of these models extends back to the works of Rudolph Peierls and Douglas R. Hofstadter, and the models themselves have been a focus of mathematical research for two decades. Jean Bourgain here sets forth the results and techniques that have been discovered in the last few years. He puts special emphasis on so-called "non-perturbative" methods and the important role of subharmonic function theory and semi-algebraic set methods. He describes various applications to the theory of differential equations and dynamical systems, in particular to the quantum kicked rotor and KAM theory for nonlinear Hamiltonian evolution equations. Intended primarily for graduate students and researchers in the general area of dynamical systems and mathematical physics, the book provides a coherent account of a large body of work that is presently scattered in the literature. It does so in a refreshingly contained manner that seeks to convey the present technological "state of the art."
410  0$aAnnals of mathematics studies ;$vNumber 158.
606   $aSchro?dinger operator
606   $aGreen's functions
606   $aHamiltonian systems
606   $aEvolution equations
610   $aAlmost Mathieu operator.
610   $aAnalytic function.
610   $aAnderson localization.
610   $aBetti number.
610   $aCartan's theorem.
610   $aChaos theory.
610   $aDensity of states.
610   $aDimension (vector space).
610   $aDiophantine equation.
610   $aDynamical system.
610   $aEquation.
610   $aExistential quantification.
610   $aFundamental matrix (linear differential equation).
610   $aGreen's function.
610   $aHamiltonian system.
610   $aHermitian adjoint.
610   $aInfimum and supremum.
610   $aIterative method.
610   $aJacobi operator.
610   $aLinear equation.
610   $aLinear map.
610   $aLinearization.
610   $aMonodromy matrix.
610   $aNon-perturbative.
610   $aNonlinear system.
610   $aNormal mode.
610   $aParameter space.
610   $aParameter.
610   $aParametrization.
610   $aPartial differential equation.
610   $aPeriodic boundary conditions.
610   $aPhase space.
610   $aPhase transition.
610   $aPolynomial.
610   $aRenormalization.
610   $aSelf-adjoint.
610   $aSemialgebraic set.
610   $aSpecial case.
610   $aStatistical significance.
610   $aSubharmonic function.
610   $aSummation.
610   $aTheorem.
610   $aTheory.
610   $aTransfer matrix.
610   $aTransversality (mathematics).
610   $aTrigonometric functions.
610   $aTrigonometric polynomial.
610   $aUniformization theorem.
615  0$aSchro?dinger operator.
615  0$aGreen's functions.
615  0$aHamiltonian systems.
615  0$aEvolution equations.
676   $a515.3/9
686   $a33.06$2bcl
700   $aBourgain$b Jean$f1954-$056557
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910790364803321
996   $aGreen's function estimates for lattice Schro?dinger operators and applications$93852862
997   $aUNINA