DOI10.1515/9781400837144zbMath1137.35001OpenAlexW4255881044MaRDI QIDQ4650421
Jean Bourgain
Publication date: 11 February 2005
Full work available at URL: https://doi.org/10.1515/9781400837144
Quasi-periodic solutions of two dimensional Schrödinger equations with quasi-periodic forcing,
Energy supercritical nonlinear Schrödinger equations: quasiperiodic solutions,
KAM for PDEs,
KAM for autonomous quasi-linear perturbations of mKdV,
Reducible quasi-periodic solutions for the non linear Schrödinger equation,
KAM for the Klein Gordon equation on \(\mathbb {S}^d\),
Homogeneity of the spectrum for quasi-periodic Schrödinger operators,
An abstract Nash-Moser theorem with parameters and applications to PDEs,
Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions,
Smooth quasi-periodic solutions for the perturbed mKdV equation,
A KAM theorem for Hamiltonian partial differential equations in higher dimensional spaces,
Birkhoff normal form for partial differential equations with tame modulus,
Small-divisor equation of higher order with large variable coefficient and application to the coupled KdV equation,
Nonlinear vibrations of a beam with time-varying rigidity and mass,
Quasi-periodic solutions in a nonlinear Schrödinger equation,
The set of smooth quasi-periodic Schrödinger cocycles with positive Lyapunov exponent is not open,
Hölder continuity of the integrated density of states for the Fibonacci Hamiltonian,
Real analytic quasi-periodic solutions with more Diophantine frequencies for perturbed KdV equations,
Continuity of the measure of the spectrum for quasiperiodic Schrödinger operators with rough potentials,
Quasi-periodic solutions with Sobolev regularity of NLS on \(\mathbb T^d\) with a multiplicative potential,
Global theory of one-frequency Schrödinger operators,
Concentration of eigenvalues for skew-shift Schrödinger operators,
Hölder continuity of absolutely continuous spectral measures for one-frequency Schrödinger operators,
Invariant tori of full dimension for second KdV equations with the external parameters,
Large coupling asymptotics for the Lyapunov exponent of quasi-periodic Schrödinger operators with analytic potentials,
Quasi-periodic solutions with prescribed frequency in a nonlinear Schrödinger equation,
An estimate on the number of eigenvalues of a quasiperiodic Jacobi matrix of size \(n\) contained in an interval of size \(n^{-C}\),
An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation,
Wegner estimates for sign-changing single site potentials,
A spectral alternative for continuous families of self-adjoint operators,
Branching of Cantor manifolds of elliptic tori and applications to PDEs,
Asymptotic Lyapunov exponents for large random matrices,
On resonances and the formation of gaps in the spectrum of quasi-periodic Schrödinger equations,
Nonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces,
Non-perturbative positive Lyapunov exponent of Schrödinger equations and its applications to skew-shift mapping,
Invariant tori of full dimension for a nonlinear Schrödinger equation,
Positive Lyapunov exponents for higher dimensional quasiperiodic cocycles,
Continuity of the Lyapunov exponents for quasiperiodic cocycles,
Quasi-periodic solutions for 1D Schrödinger equation with the nonlinearity \(|u|^{2p}u\),
Quasiperiodic solutions of completely resonant wave equations with quasiperiodic forced terms,
Linearly stable quasi-periodic breathers in a class of random Hamiltonian systems,
Complex one-frequency cocycles,
Quasi-periodic solutions with prescribed frequency in reversible systems,
All couplings localization for quasiperiodic operators with monotone potentials,
Mini-workshop: Reflectionless operators: the Deift and Simon conjectures. Abstracts from the mini-workshop held October 22--28, 2017,
Pure point spectrum of the Floquet Hamiltonian for the quantum harmonic oscillator under time quasi-periodic perturbations,
Anderson localization for two interacting quasiperiodic particles,
The spectrum of skew-shift Schrödinger operators contains intervals,
KAM Tori for higher dimensional quintic beam equation,
Positivity of the top Lyapunov exponent for cocycles on semisimple Lie groups over hyperbolic bases,
Time quasi-periodic gravity water waves in finite depth,
The stability of full dimensional KAM tori for nonlinear Schrödinger equation,
Construction of periodic solutions for nonlinear wave equations by a para-differential method,
A KAM theorem for higher dimensional forced nonlinear Schrödinger equations,
A KAM theorem for space-multidimensional Hamiltonian PDEs,
Non-perturbative localization with quasiperiodic potential in continuous time,
Generic continuous spectrum for ergodic Schrödinger operators,
Quasi-periodic solutions of forced Kirchhoff equation,
Periodic solutions for the Schrödinger equation with nonlocal smoothing nonlinearities in higher dimension,
A lower bound on the Lyapunov exponent for the generalized Harper's model,
Continuity of Lyapunov exponent for analytic quasi-periodic cocycles on higher-dimensional torus,
Continuity, positivity and simplicity of the Lyapunov exponents for quasi-periodic cocycles,
A normal form for the Schrödinger equation with analytic non-linearities,
Anderson localization for the discrete one-dimensional quasi-periodic Schrödinger operator with potential defined by a Gevrey-class function,
Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation,
Quasi-periodic solutions for two dimensional modified Boussinesq equation,
KAM for the nonlinear Schrödinger equation,
Zero Hausdorff dimension spectrum for the almost Mathieu operator,
Invariant tori of a nonlinear Schrödinger equation with quasi-periodically unbounded perturbations,
Lyapunov exponents of discrete quasi-periodic Gevrey Schrödinger equations,
KAM for the nonlinear beam equation,
Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts,
Quasi-periodic breathers in Hamiltonian networks of long-range coupling,
Fixed point theory approach to boundary value problems for second-order difference equations on non-uniform lattices,
Weyl sums and the Lyapunov exponent for the skew-shift Schrödinger cocycle,
Uniform hyperbolicity and its relation with spectral analysis of 1D discrete Schrödinger operators,
Invariant tori for commuting Hamiltonian PDEs,
Almost-periodic response solutions for a forced quasi-linear Airy equation,
A KAM theorem for the Hamiltonian with finite zero normal frequencies and its applications (in memory of Professor Walter Craig),
Absence of eigenvalues of analytic quasi-periodic Schrödinger operators on \({\mathbb{R}}^d\),
On the spectra of separable 2D almost Mathieu operators,
Invariant tori of nonlinear Schrödinger equation,
An approach to Wegner's estimate using subharmonicity,
Quasi-periodic solutions for the generalized Benjamin-Bona-Mahony equation,
Quantitative lower bounds on the Lyapunov exponent from multivariate matrix inequalities,
A KAM theorem for the defocusing NLS equation,
Almost periodic solutions for a class of higher dimensional Schrödinger equations,
Long time stability result for 1-dimensional nonlinear Schrödinger equation,
Linearly stable KAM tori for higher dimensional Kirchhoff equations,
Anderson localization for multi-frequency quasi-periodic operators on \(\mathbb{Z}^d\),
Anderson localization for a generalized Maryland model with potentials given by skew shifts,
On long time existence for small solutions of semi-linear Klein-Gordon equations on the torus,
Quasi-periodic solutions of nonlinear wave equations with quasi-periodic forcing,
Almost global solutions to Hamiltonian derivative nonlinear Schrödinger equations on the circle,
A family of Schrödinger operators whose spectrum is an interval,
Normal forms for semilinear quantum harmonic oscillators,
Invariant tori for a two-dimensional completely resonant beam equation with a quintic nonlinear term,
Almost periodic Szegő cocycles with uniformly positive Lyapunov exponents,
Lyapunov exponents for discrete, quasi-periodic Schrödinger operators,
Positivity and continuity of the Lyapunov exponent for shifts on \(\mathbb T^d\) with arbitrary frequency vector and real analytic potential,
An introduction to multiscale techniques in the theory of Anderson localization. I,
Quantitative reducibility of Gevrey quasi-periodic cocycles and its applications,
A separation lemma on sub-lattices,
Quasi-periodic solutions for perturbed generalized KdV equation,
Long time dynamics of Schrödinger and wave equations on flat tori,
Invariant Cantor manifolds of quasi-periodic solutions for the derivative nonlinear Schrödinger equation,
Hölder regularity of the integrated density of states for quasi-periodic long-range operators on \(\ell^2(\mathbb{Z}^d)\),
A KAM theorem for higher dimensional nonlinear Schrödinger equations,
Positive Lyapunov exponent for some Schrödinger cocycles over multidimensional strongly expanding torus endomorphisms,
Stability of KAM tori for nonlinear Schrödinger equation,
Construction of quasi-periodic solutions for nonlinear forced perturbations of dissipative Boussinesq systems,
A KAM theorem with applications to partial differential equations of higher dimensions,
Periodic solutions for a class of nonlinear partial differential equations in higher dimension,
Quasi-periodic solutions of fractional nonlinear Schrödinger equation systems,
On the quasi-periodic solutions for generalized Boussinesq equation with higher order nonlinearity,
The repetition property for sequences on tori generated by polynomials or skew-shifts,
Approximate normal forms via Floquet-Bloch theory: Nehorošev stability for linear waves in quasiperiodic media,
KAM theory for the reversible perturbations of 2D linear beam equations,
KAM tori for defocusing modified KDV equation,
The existence of full dimensional invariant tori for 1-dimensional nonlinear wave equation,
Bounded Sobolev norms for Klein-Gordon equations under non-resonant perturbation,
Sharp \(\frac{1}{2}\)-Hölder continuity of the Lyapunov exponent at the bottom of the spectrum for a class of Schrödinger cocycles,
Bounded non-response solutions with Liouvillean forced frequencies for nonlinear wave equations,
Unbounded trace orbits of Thue-Morse Hamiltonian,
Time periodic solutions of one-dimensional forced Kirchhoff equation with Sturm-Liouville boundary conditions,
The existence of solutions for nonlinear elliptic equations: simple proofs and extensions of a paper by Y. Shi,
An infinite dimensional KAM theorem with application to two dimensional completely resonant beam equation,
Quasi-periodic solutions of derivative beam equation on flat tori,
Quasi-periodic solutions for a class of higher dimensional beam equation with quasi-periodic forcing,
Quasi-periodic solutions of a fractional nonlinear Schrödinger equation,
Spectral theory of the multi-frequency quasi-periodic operator with a Gevrey type perturbation,
Space quasi-periodic standing waves for nonlinear Schrödinger equations,
Anderson localization for Jacobi matrices associated with high-dimensional skew shifts,
Quasi-Periodic Standing Wave Solutions of Gravity-Capillary Water Waves,
Schrödinger operators with dynamically defined potentials,
Dynamics and spectral theory of quasi-periodic Schrödinger-type operators,
Localization for random operators with non-monotone potentials with exponentially decaying correlations,
Large coupling asymptotics for the entropy of quasi-periodic operators,
Quantitative inductive estimates for Green's functions of non-self-adjoint matrices,
Point spectrum of the Floquet Hamiltonian for Klein-Gordon equation under quasi-periodic perturbations,
KAM for the derivative nonlinear Schrödinger equation with periodic boundary conditions,
On optimal separation of eigenvalues for a quasiperiodic Jacobi matrix,
Quasi-periodic solution of nonlinear beam equation on \(\mathbb{T}^d\) with forced frequencies,
Strange nonchaotic attractors in Harper maps,
Arithmetic version of Anderson localization via reducibility,
On quasi-periodic solutions for a generalized Boussinesq equation,
KAM tori for completely resonant Hamiltonian derivative beam equations on \(\mathbb{T}^2\),
Quasi-periodic solutions of Schrodinger equations with quasi-periodic forcing in higher dimensional spaces,
Cantor spectrum and KDS eigenstates,
Global eigenvalue distribution of matrices defined by the skew-shift,
Unnamed Item,
Dynamics of the quasi-periodic Schrödinger cocycle at the lowest energy in the spectrum,
Cantor families of periodic solutions for wave equations via a variational principle,
On the inverse spectral problem for the quasi-periodic Schrödinger equation,
Lower dimensional invariant tori with prescribed frequency for the nonlinear Schrödinger equation,
Long-Time Existence for Semi-Linear Klein–Gordon Equations with Quadratic Potential,
Localization for quasiperiodic Schrödinger operators with multivariable Gevrey potential functions,
An abstract Nash-Moser theorem and quasi-periodic solutions for NLW and NLS on compact Lie groups and homogeneous manifolds,
Quasiperiodic motions in dynamical systems: Review of a renormalization group approach,
A Nash-Moser Approach to KAM Theory,
Quasi-periodic solutions for the forced Kirchhoff equation on $ \newcommand{\m}{\mu} \newcommand{\T}{\mathbb T} \T^d$,
Mixed spectral types for the one-frequency discrete quasi-periodic Schrödinger operator,
Analytic solutions of nonlinear elliptic equations on rectangular tori,
Time periodic solutions of one-dimensional forced Kirchhoff equations with \(x\)-dependent coefficients under spatial periodic conditions,
Large deviation type estimates for iterates of linear cocycles,
Anderson localization for the completely resonant phases,
On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data,
Periodic and quasi-periodic solutions of a derivative nonlinear Schrödinger equation,
ON THE EXISTENCE OF FULL DIMENSIONAL KAM TORUS FOR FRACTIONAL NONLINEAR SCHRÖDINGER EQUATION,
A KAM theorem for higher dimensional wave equations under nonlocal perturbation,
Finite dimensional invariant KAM tori for tame vector fields,
Effective multi-scale approach to the Schrödinger cocycle over a skew-shift base,
Hölder continuity of absolutely continuous spectral measure for multi-frequency Schrödinger operators,
Construction of quasi-periodic solutions for delayed perturbation differential equations,
On the spectrum of multi-frequency quasiperiodic Schrödinger operators with large coupling,
On the existence of Sobolev quasi-periodic solutions of multidimensional nonlinear beam equation,
Large coupling asymptotics for the Lyapunov exponent of finitely smooth quasi-periodic Schrödinger operators,
Continuity of the Lyapunov exponent for analytic quasiperiodic cocycles,
Full dimension tori of Schrödinger equation,
Construction of quasi-periodic solutions for the quintic Schrödinger equation on the two-dimensional torus $\mathbb {T}^2$,
THE ENERGY GRAPH OF THE NONLINEAR SCHRÖDINGER EQUATION, OPEN PROBLEMS,
The arithmetic version of the frequency transition conjecture: new proof and generalization,
Global rigidity for ultra-differentiable quasiperiodic cocycles and its spectral applications,
Upper bounds on transport exponents for long-range operators,
KAM tori for generalized Benjamin-Ono equation,
Hölder continuity of the Lyapunov exponents of linear cocycles over hyperbolic maps,
Anderson localization for multi-frequency quasi-periodic Jacobi operators,
Multiscale analysis for ergodic Schrödinger operators and positivity of Lyapunov exponents,
Spectral gaps of almost Mathieu operators in the exponential regime,
A KAM result on compact Lie groups,
Anderson localization for the almost Mathieu operator in the exponential regime,
Invariant tori for a nonlinearly modified Kawahara equation with periodic boundary conditions,
Bounds on the Lyapunov exponent via crude estimates on the density of states,
KAM tori for the two-dimensional completely resonant Schrödinger equation with the general nonlinearity,
Quasi-periodic solutions for fully nonlinear forced reversible Schrödinger equations,
Quasi-periodic solutions for nonlinear wave equations,
Reducible KAM tori for two-dimensional nonlinear Schrödinger equations with explicit dependence on the spatial variable,
Melnikov-type theorem for time reversible system,
Quasi-periodic solutions of PDEs,
Anderson localization for one-frequency quasi-periodic block Jacobi operators,
Quasiperiodic solutions to nonlinear random Schrödinger equations at fixed potential realizations,
Power law logarithmic bounds of moments for long range operators in arbitrary dimension,
Cartan Covers and Doubling Bernstein-Type Inequalities on Analytic Subsets of $$\mathbb {C}^2$$,
Logarithmic Quantum Dynamical Bounds for Arithmetically Defined Ergodic Schrödinger Operators with Smooth Potentials,
Unnamed Item,
Anderson localization for the quasi-periodic CMV matrices with Verblunsky coefficients defined by the skew-shift,
Homogeneous spectrum of quasi-periodic Gevrey Schrödinger operators with Diophantine frequency,
A KAM algorithm for two-dimensional nonlinear Schrödinger equations with spatial variable,
Stability of spectral types of quasi-periodic Schrödinger operators with respect to perturbations by decaying potentials,
On the Lyapunov exponent for some quasi-periodic cocycles with large parameter,
Response solutions for KdV equations with Liouvillean frequency,
An asymptotic formula for the Lyapunov exponent of Gevrey skew-shift Schrödinger operator,
Quasi-periodic solution of quasi-linear fifth-order KdV equation,
Upper bounds on quantum dynamics in arbitrary dimension,
A “lifting” method for exponential large deviation estimates and an application to certain non-stationary 1D lattice Anderson models,
Spectral characteristics of Schrödinger operators generated by product systems,
Quasi-periodic solutions for a generalized higher-order Boussinesq equation,
Time quasi-periodic vortex patches of Euler equation in the plane,
Localization for almost-periodic operators with power-law long-range hopping: a Nash-Moser iteration type reducibility approach,
Quantitative version of Gordon's lemma for Hamiltonian with finite range,
Stability and recursive solutions in Hamiltonian PDEs,
Hölder continuity of Lyapunov exponent for a family of smooth Schrödinger cocycles,
Pointwise modulus of continuity of the Lyapunov exponent and integrated density of states for analytic multi-frequency quasi-periodic M(2,C) cocycles,
Quasi-periodic solutions for differential equations with an elliptic equilibrium under delayed perturbation,
A KAM theorem for two dimensional completely resonant reversible Schrödinger systems,
Exact mobility edges for 1D quasiperiodic models,
Exponential Dynamical Localization: Criterion and Applications,
Quasi-periodic Solutions for Schrödinger Equation with Finite Smooth Quasi-periodic Forcing,
Almost Mathieu operators with completely resonant phases,
Spacetime quasiperiodic solutions to a nonlinear Schrödinger equation on Z,
One-dimensional quasiperiodic operators: global theory, duality, and sharp analysis of small denominators,
Linearly stable KAM tori for one dimensional forced Kirchhoff equations with refined Töplitz-Lipschitz property,
Invariant tori for two-dimensional nonlinear Schrödinger equations with large forcing terms,
Extended States for the Schrödinger Operator with Quasi-periodic Potential in Dimension Two,
Reducible KAM tori for higher dimensional wave equations under nonlocal and forced perturbation,
Multiscale analysis in momentum space for quasi-periodic potential in dimension two,
On Zaremba's conjecture,
On quasi-periodic solutions for generalized Boussinesq equation with quadratic nonlinearity,
Periodic solutions of the generalized KdV equation,
Anderson localization for one-frequency quasi-periodic block operators with long-range interactions,
Hölder continuity of the spectral measures for one-dimensional Schrödinger operator in exponential regime,
Invariant tori for a derivative nonlinear Schrödinger equation with quasi-periodic forcing,
Quasi-periodic solutions for d-dimensional beam equation with derivative nonlinear perturbation,
Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres,
Quasi-Periodic Solutions of Nonlinear Wave Equation with x-Dependent Coefficients,
Semi-algebraic sets method in PDE and mathematical physics,
Anderson localization for long-range operators with singular potentials,
On the Control Problem for Schrödinger Operators on Tori